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Page No 85:

Question 1:

Mark the correct alternative in each of the following:

The point of intersect of the coordinate axes is

(a) ordinate

(b) abscissa

(c) quadrant

(d) origin

Answer:

As we know that:

The distance of a point from y−axis is called its x−coordinate or abscissa.

The distance of a point from x−axis is called its y−coordinate or ordinate.

The coordinate axes divide the plane into four equal parts which are known as quadrants.

The point of intersection of the coordinate axes is called the origin and the coordinates of origin are.

Example is shown in the graph 

Thus the correct answer is (d).

Page No 85:

Question 2:

The abscissa and ordinate of the origin are

(a) (0, 0)

(b) (1, 0)

(c) (0, 1)

(d) (1, 1)

Answer:

As we know that:

The distance of a point from y−axis is called its x−coordinate or abscissa.

The distance of a point from x−axis is called its y−coordinate or ordinate.

The coordinate axes divide the plane into four equal parts which are known as quadrants.

The point of intersection of the coordinate axes is called the origin and the coordinates of origin are.

The origin is shown in the graph 

Thus the correct answer is (a).

Page No 85:

Question 3:

The measure of the angle between the coordinate axes is

(a) 0°

(b) 90°

(c) 180°

(d) 360°

Answer:

As we know that x−axis and y−axis intersect to each other at point O and perpendicular to each other. So, the angle between the coordinate axes is.

Thus the correct answer is (b).

Page No 85:

Question 4:

A point whose abscissa and ordinate are 2 and −5 respectively, lies in

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

Answer:

As shown in graph that a point whose abscissa and ordinate areand respectively lies in the fourth quadrant.

Thus the correct answer is (d).

Page No 85:

Question 5:

Points (−4, 0) and (7, 0) lie

(a) on x-axis

(b) y-axis

(c) in first quadrant

(d) In second quadrant

Answer:

Let the points P and Q whose coordinates are andrespectively. Locate the points and you will see that they lie on x-axis.

Thus the correct answer is (a).

Page No 85:

Question 6:

The ordinate of any point on x-axis is

(a) 0

(b) 1

(c) −1

(d) any number

Answer:

We know that the y−coordinates of every point on x−axis are zero. So, the coordinates of any point on the x−axis are of the form.

Thus the correct answer is (a).

Page No 85:

Question 7:

The abscissa of any point on y-axis is

(a) 0

(b) 1

(c) −1

(d) any number

Answer:

We know that the x−coordinate of every point on y-axis is zero. So, the coordinates of any point on the x−axis are of the form.

Thus the correct answer is (a).

Page No 85:

Question 8:

The abscissa of a point is positive in the

(a) First and Second quadrant

(b) Second and Third quadrant

(c) Third and Fourth quadrant

(d) Fourth and First quadrant

Answer:

The signs of coordinates of a point in various quadrants are shown in the following graph:

Thus the correct answer is (d).

Page No 85:

Question 9:

A point whose abscissa is −3 and ordinate 2 lies in

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

Answer:

As we know that

In the first quadrant

In the second quadrant

In the third quadrant

In the fourth quadrant

The point whose abscissa is −3 which is negative and ordinate 2 is positive, so this point lies in the second quadrant.

Thus the correct answer is (b).

Page No 85:

Question 10:

Two points having same abscissae but different ordinate lie on

(a) x-axis

(b) y-axis

(c) a line parallel to y-axis

(d) a line parallel to x-axis

Answer:

Let the points and having the same abscissa but different ordinates be shown in the graph given below:

Fig: (location of two considered points)

And these points lie on a line parallel to y−axis

Thus the correct answer is (c).

Page No 85:

Question 11:

The perpendicular distance of the point P (4, 3) from x-axis is

(a) 4

(b) 3

(c) 5

(d) none of these

Answer:

The point is shown in the graph given below: 

Thus the perpendicular distance of the point from x−axis is 3 units.

Thus the correct answer is (b).

Page No 85:

Question 12:

The perpendicular distance of the P (4,3)  from y-axis is

(a) 4

(b) 3

(c) 5

(d) none of these

Answer:

The point is shown in the graph given below: 

Thus the perpendicular distance of the point from y−axis is 4.

Thus the correct answer is (a).

Page No 85:

Question 13:

The points (other than origin) for which abscissa is equal to the ordinate will lie in
(a) I quadrant only
(b) I and II quadrants
(c) I and III quadrants
(d) II and IV quadrants

Answer:


In I quadrant: x > 0, y > 0

In II quadrant: x < 0, y > 0

In III quadrant: x < 0, y < 0

In IV quadrant: x > 0, y < 0

The points for which abscissa is equal to the ordinate, both x and y must be of same sign i.e. either x > 0, y > 0 or x < 0, y < 0.

The co-ordinates of the points for which abscissa is equal to the ordinate are of the form (x, y) or (−x, −y), where x = y.

Thus, the points (other than origin) for which abscissa is equal to the ordinate will lie in I and III quadrants.

Hence, the correct answer is option (c).



Page No 86:

Question 14:

Signs of the abscissa and ordinate of a point in the second quadrant are respectively
(a) +, +
(b) –, –
(c) –, +
(d) +, –

Answer:


In the second quadrant, x < 0, y > 0.

Thus, the signs of the abscissa and ordinate of a point in the second quadrant are negative and positive, respectively. That is, x is − and y is +.

Hence, the correct answer is option (c).

Page No 86:

Question 15:

Abscissa of all points on the x-axis is
(a) 0
(b) 1
(c) 2
(d) any number

Answer:


The co-ordinate of a point on the x-axis are of the form (x, 0).  So, the abscissa of all points on the x-axis is any number.

Hence, the correct answer is option (d).

Page No 86:

Question 16:

Ordinate of all points on the y-axis is
(a) 0
(b) 1
(c) 2
(d) any number

Answer:


Disclaimer: The answer has been provided for the following question.

Abscissa of all points on the y-axis is
(a) 0
(b) 1
(c) 2
(d) any number

Solution:

If we take any point on the y-axis, then the distance of this point from the y-axis is 0. Therefore, the abscissa of this point is 0. 

The co-ordinate of a point on the y-axis are of the form (0, y). So, the abscissa of all points on the y-axis is 0.

Hence, the correct answer is option (a).

Page No 86:

Question 17:

A point whose abscissa and ordinate both are negative will lie in
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant

Answer:


In the third quadrant, x < 0, y < 0. Thus, the point whose abscissa and ordinate both are negative will lie in III quadrant.

Hence, the correct answer is option (c).

Page No 86:

Question 18:

Points (2, –2), (3, –3), (4, –5), (–3, –4)
(a) lie in II quadrant
(b) lie in III quadrant
(c) lie in IV quadrant
(d) do not lie in the same quadrant

Answer:


The given points are (2, –2), (3, –3), (4, –5) and (–3, –4).

In the third quadrant: x < 0, y < 0

So, the point (–3, –4) lie in the III quadrant.

In the fourth quadrant: x > 0, y < 

So, the points (2, –2), (3, –3), (4, –5) lie in the IV quadrant.

Thus, the given points (2, –2), (3, –3), (4, –5), (–3, –4) do not lie in the same quadrant.

Hence, the correct answer is option (d).

 

Page No 86:

Question 19:

The points whose abscissa and ordinate have different signs will lie in
(a) I and II quadrants
(b) II and III quadrants
(c) I and III quadrants
(d) II and IV quadrants

Answer:


In I quadrant: x > 0, y > 0

In II quadrant: x < 0, y > 0

In III quadrant: x < 0, y < 0

In IV quadrant: x > 0, y < 0

The abscissa and ordinate have the same sign in I and III quadrants whereas the abscissa and ordinate have different signs in II and IV quadrants.

Thus, the points whose abscissa and ordinate have different signs will lie in II and IV quadrants.

Hence, the correct answer is option (d).

Page No 86:

Question 20:

Abscissa of a point is positive in
(a) I and II quadrants
(b) I and IV quadrants
(c) I quadrant only
(d) II quadrant only

Answer:


In I quadrant: x > 0, y > 0

In II quadrant: x < 0, y > 0

In III quadrant: x < 0, y < 0

In IV quadrant: x > 0, y < 0

Thus, the abscissa of the point is positive (x > 0) in I and IV quadrants.

Hence, the correct answer is option (b).

Page No 86:

Question 21:

On plotting the points O(0, 0), A(3, 0), B(3, 4), C(0, 4) and joining OA, AB, BC and CO which of the following figure is formed?
(a) Square
(b) Rectangle
(c) Trapezium
(d) Rhombus

Answer:


The given points are O(0, 0), A(3, 0), B(3, 4) and C(0, 4).  These points can be plotted on the graph paper as shown below.



From the figure, we have

OA = 3 units, AB = 4 units, BC = 3 units and OC = 4 units

In quadrilateral OABC,

OA = BC = 3 units and AB = OC = 4 cm

Thus, the quadrilateral OABC is a rectangle.

Hence, the correct answer is option (b).

Page No 86:

Question 22:

The image of the point (3, 4) in x-axis has the coordinates
(a) (–3, 4)
(b) (3, –4)
(c) (–3, –4)
(d) (4, 3)

Answer:


Under reflection of a point in the x-axis, the abscissa of the point remains unchanged while the sign of the ordinate is changed. So, the image of the point (x, y) in the x-axis is (x, −y).

Thus, the image of the point (3, 4) in the x-axis is (3, −4).

Hence, the correct answer is option (b).

Page No 86:

Question 23:

The image of the point (–5, 7) in y-axis has the coordinates
(a) (5, 7)
(b) (–5, –7)
(c) (5, –7)
(d) (7, –5)

Answer:


Under reflection of a point in the y-axis, the ordinate of the point remains unchanged while the sign of the abscissa is changed. So, the image of the point (x, y) in the y-axis is (−x, y).

Thus, the image of the point (−5, 7) in the y-axis is (5, 7).

Hence, the correct answer is option (a).

Page No 86:

Question 24:

If the perpendicular distance of a point P from the x-axis is 5 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has
(a) x-coordinate 5
(b) y-coordinate = 5 only
(c) y-coordinate = – 5 only
(d) y-coordinate = 5 or –5

Answer:


The perpendicular distance of a point from the x-axis gives the ordinate of the point. It is given that the foot of the perpendicular lies on the negative direction of x-axis, so the perpendicular distance can be measured in II or III quadrant.

It is given that, the perpendicular distance of a point P from the x-axis is 5 units and the foot of perpendicular lies on the negative direction of x-axis. So, the point P can be plotted on the graph paper as shown below.



Thus, the point P has y-coordinate as 5 or −5.

Hence, the correct answer is option (d).

Page No 86:

Question 25:

If the mirror image of the point P(5, 2) in x-axis is the point Q and the image of Q in y-axis is R. Then the coordinates of R are
(a) (5, –2)
(b) (–5, –2)
(c) (–5, 2)
(d) (2, 5)

Answer:


Under reflection of a point in the x-axis, the abscissa of the point remains unchanged while the sign of the ordinate is changed. So, the image of the point (x, y) in the x-axis is (x, −y).

So, the image of the point P(5, 2) in x-axis is Q(5, −2).

Now, under reflection of a point in the y-axis, the ordinate of the point remains unchanged while the sign of the abscissa is changed. So, the image of the point (x, y) in the y-axis is (−x, y).

So, the image of the point Q(5, −2) in y-axis is R(−5, −2).

Thus, the co-ordinates of the point R are (−5, −2).

Hence, the correct answer is option (b).

Page No 86:

Question 26:

The distance of the point P (4, 3) from the origin is

(a) 4

(b) 3

(c) 5

(d) 7

Answer:

The point is shown in the graph given below: 

In is right angled triangle where

By using Pythagoras theorem:

 

Thus the distance of the pointfrom the origin is 5.

Thus the correct answer is (c)

Page No 86:

Question 27:

The area of the triangle formed by the points A(2,0) B(6,0)  and C(4,6) is

(a) 24 sq. units

(b) 12 sq. units

(c) 10 sq. units

(d) none of these

Answer:

Given that points A, Band Cform a triangle which is shown in the figure. We are asked to find the area of the triangle ΔABC.

Given that 

Hence:

AB=OB-OA=6-2=4
CD = 6

By using formula,

ABC=12×AB×CD=12×4×6=12 sq units

Thus the correct answer is (b).

Page No 86:

Question 28:

The area of the triangle formed by the points P (0, 1), Q (0, 5) and R (3, 4) is

(a) 16 sq. units

(b) 8 sq. units

(c) 4 sq. units

(d) 6 sq. units

Answer:

Given that the points,and form a triangle.

We are asked to find the area of the triangle ΔPQR which is shown in the figure.

Given that 

Hence

By using formula,

Thus the correct answer is (d).

Page No 86:

Question 29:

The area of the triangle formed by the point P(–3, 4) and its reflections in the coordinate axes is 
(a) 24 sq. units
(b) 48 sq. units
(c) 16 sq. units
(d) 12 sq. units

Answer:

We have, P(–3, 4) in the coordinate axis.
Reflection of P(–3, 4) in the x-axis will give A(–3, –4).
Also, the Reflection of P(–3, 4) in the y-axis will give B(3, 4).
Therefore, the required triangle will be

 Area of triangle APB=12×AP×PB=12×8×6=24 sq. units

Hence, the correct answer is option (a).



Page No 87:

Question 30:

The distance between the reflections of the point P(–3, 4) in the coordinate axes is 
(a) 8 units
(b) 6 units
(c) 14 units
(d) 10 units

Answer:

Given that, P(–3, 4) in the coordinate axes 
Reflection of P(–3, 4) in the x-axes = A(–3, –4)
Reflection of P(–3, 4) in the y-axes = B(3, 4)
Distance between points A and B=4--42+3--32=64+36=100=10 units

Hence, the correct answer is option (d).

Page No 87:

Question 31:

The quadrilateral formed by joining the points A(0, 0), B(5, 0), C(3, 2) and D(0, 2) in order is a 
(a) square
(b) parallelogram
(c) trapezium
(d) rectangle

Answer:

The points A(0, 0), B(5, 0), C(3, 2) and D(0, 2) when plotted, the following is obtained:

The figure obtained is a trapezium, as the pair of opposite sides are not of equal length.
AB = 5 units
CD = 3 units 
And, AD is not parallel to BC.

Hence, the correct answer is option (c).

Page No 87:

Question 32:

The area of the figure ABCD formed by joining A(–1, 1), B(5, 1), C(5, 6) and D(–1, 6) is
(a) 40 sq. units
(b) 30 sq. units
(c) 20 sq. units
(d) 16 sq. units

Answer:

Here, the points A(–1, 1), B(5, 1), C(5, 6), and D(–1, 6) when plotted, the following is obtained:

The figure obtained is a rectangle. This is because
AB = CD = 6 units
AD = BC = 5 units
and the opposite sides are parallel to each other.

 Area of rectangle = AB×BC
                                 = 6×5
                                 = 30 sq. units

Hence, the correct answer is option (b).

Page No 87:

Question 33:

The distance between the points A(–5, 12) and (7, 12) is
(a) 5 units
(b) 7 units
(c) 12 units
(d) 17 units

Answer:

The given points A(–5, 12) and (7, 12) lie in the II and I quadrants respectively.
Therefore, the distance between points A and B
7--5            (∵ y coordinates will remain same)
= 12 units

Hence, the correct answer is an option (c).

Page No 87:

Question 34:

The distance between the images of points P(–7, 4) and Q(7, 4) in x-axis is 
(a) 7 units
(b) 8 units
(c) 11 units
(d) 14 units

Answer:

The given points P(–7, 4) and Q(7, 4) lie in the II and I quadrants respectively.
Therefore, the distance between points P and Q
7--7            (∵ y coordinates will remain the same)
= 14 units

Hence, the correct answer is option (d).

Page No 87:

Question 35:

The distance of the point P(–6, 8) from the origin is
(a) 6 units
(b) 8 units
(c) 10 units
(d) 14 units

Answer:

The coordinates of the origin are O(0, 0).
Since the distance between points Ax1,y1 and Bx2,y2 x2-x12+y2-y12
Here, P(–6, 8) and O(0, 0)
Distance of the point P from origin O = PO
 PO=0+62+0-82=62+-82=36+64=100=10 units

Thus, the distance of the point P(–6, 8) from the origin is 10 units.
Hence, the correct answer is option (c).

Page No 87:

Question 36:

If the point P(4, 2) is translated parallel to x-axis through 8 units, then the coordinates of new position of P are
(a) (4, 10)
(b) (4, 6)
(c) (12, 2)
(d) (4, –6)

Answer:

If the point P(4, 2) is translated parallel to the x-axis then its y coordinates will remain constant and the new x coordinate will move through 8 units.
The coordinates of the new position of = (4, 2)
= (4 +8, 2)
= (12, 2)

Hence, the correct answer is option (c).

Page No 87:

Question 37:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): The point P(–7, 0) lies on x-axis.
Statement-2 (Reason): The ordinate of every point on y-axis is positive.

Answer:

Statement-2 (Reason): The ordinate of every point on y-axis is positive.
​
The coordinate of a point on the y-axis is of the form B0, b, where b can be positive or negative.
So, the ordinate of every point on y-axis can be positive or negative.

Thus, Statement-2 is false. 

Statement-1 (Assertion): The point P(–7, 0) lies on x-axis.
Any point of the form Aa, 0 always lies on the x-axis.
Thus, for point P(–7, 0), a=-7
P(–7, 0) lies on the x-axis.

Thus, Statement-1 is true. 
So, Statement-1 is true, Statement-2 is false.

Hence, the correct answer is option (c).

Page No 87:

Question 38:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): The point P(0, 12) lies on y-axis.
Statement-2 (Reason): The abscissa of every point on y-axis is zero.

Answer:

Statement-2 (Reason): The abscissa of every point on y-axis is zero.
The coordinate of a point on the y-axis is of the form B0, b, where b can be positive or negative.
∴ The abscissa of every point on the y-axis is zero.
Thus, Statement-2 is true.

Statement-1 (Assertion): The point P(0, 12) lies on y-axis.
According to Statement-2, any point of the form B0, b always lies on the y-axis.
Thus, for point P(0, 12), b=12
∴ P(0, 12) lies on the y-axis.

Thus, Statement-1 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Hence, the correct answer is option (a).

Page No 87:

Question 39:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): The perpendicular distance of the point (3, –7) from x-axis is 3.
Statement-2 (Reason): The perpendicular distance of the point (x, y) from x-axis |y|.

Answer:

Statement-2 (Reason): The perpendicular distance of the point (xy) from x-axis |y|.
The y-coordinate of a point is the perpendicular distance of the point from the x-axis.
So, âˆ£y∣ is the distance.

The absolute value is considered as the coordinates may be negative and distance should be positive.

Thus, Statement-2 is true.

Statement-1 (Assertion): The perpendicular distance of the point (3, –7) from x-axis is 3.

According to Statement-2, the perpendicular distance of the point (3, –7) from the x-axis = |–7| units = 7 units  
                                                                                                                                                   
Thus, Statement-1 is false.
So, Statement-1 is false, Statement-2 is true.

Hence, the correct answer is option (d).

Page No 87:

Question 40:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has the following four choices (a), (b), (c), and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): The coordinates of a point whose ordinate is –2 and abscissa are 5 are (–2, 5).
Statement-2 (Reason): The coordinates of a point lying on the positive x-axis at a distance of 9 units from the origin are (9, 0).

Answer:

Statement-2 (Reason): The coordinates of a point lying on the positive x-axis at a distance of 9 units from the origin are (9, 0).

The coordinate of a point on the x-axis is of the form a, 0, where a can be positive or negative and a is the perpendicular distance from the y-axis, i.e., abscissa.
∴ The coordinates of a point lying on the positive x-axis at a distance of 9 units from the origin are (9, 0).

Thus, Statement-2 is true.

Statement-1 (Assertion): The coordinates of a point whose ordinate is –2 and abscissa are 5 are (–2, 5).

Any point on the coordinate plane is well defined by an ordered pair where the ordered pair is written as (xy), where x-coordinate represents a point on the x-axis or perpendicular distance from the y-axis, i.e., abscissa and y-coordinate represents a point on the y-axis or perpendicular distance from the x-axis, i.e., ordinate.

∴ The abscissa of the point (–2, 5) = –2 and ordinate of the point (–2, 5) = 5.
                                                                                                                                                   
Thus, Statement-1 is false.
So, Statement-1 is false, Statement-2 is true.

Hence, the correct answer is option (d).

Page No 87:

Question 41:

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has the following four choices (a), (b), (c), and (d), only one of which is the correct answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) ​Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion): Points (3, –3) and (12, –4) lie in the same quadrant.
Statement-2 (Reason): Points (–1, –1) and (7, 7) lie on the bisectors of the third and first quadrant angles.

Answer:


Statement-2 (Reason): Points (–1, –1) and (7, 7) lie on the bisectors of the third and first quadrant angles.

Constructing the bisectors of the third and first quadrant angles and then plotting the points (–1, –1) and (7, 7), we get that the given points lie on the bisectors of the third and first quadrant.

Thus, Statement-2 is true.

Statement-1 (Assertion): Points (3, –3) and (12, –4) lie in the same quadrant.
Any point of the form (a, –b) lies in the IV quadrant.
∴ Points (3, –3) and (12, –4) lie in the IV quadrant.
Thus, Statement-1 is true.
So, Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

Hence, the correct answer is option (b).


 



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