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#### Question 1:

Plot the following points on the graph paper:

(i) (2,5)

(ii) (4, −3)

(iii) (−5, −7)

(iv) (7, −4)

(v) (−3, 2)

(vi) (7, 0)

(vii) (−4, 0)

(viii) (0, 7)

(ix) (0, −4)

(x) (0, 0)

The following points are given below.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Letand be the coordinate axes.

(i) Here for the given point the abscissa is 2 units and ordinate is 5 units.

The point is in the first quadrant. So it will look like as shown in the following figure.

(ii) Here for the given point the abscissa is 4 units and ordinate is -3 units.

The point is in the fourth quadrant. So it will look like as shown in the following figure.

(iii) Here for the given point the abscissa is -5 units and ordinate is -7 units.

The point is in the third quadrant. So it will look like as shown in the following figure.

(iv) Here for the given point the abscissa is 7 units and ordinate is -4 units.

The point is in the fourth quadrant. So it will look like as shown in the following figure.

(v) Here for the given point the abscissa is -3 units and ordinate is 2 units.

The point is in the second quadrant. So it will look like as shown in the following figure.

(vi) Here for the given point the abscissa is 7 units and ordinate is 0 units.

The point is on the x-axis. So it will look like as shown in the following figure.

(vii) Here for the given point the abscissa is -4 units and ordinate is 0 units.

The point is on the x-axis. So it will look like as shown in the following figure.

(viii) Here for the given point the abscissa is 0 units and ordinate is 7 units.

The point is on the y-axis. So it will look like as shown in the following figure.

(ix) Here for the given point the abscissa is 0 units and ordinate is -4 units.

The point is on the y-axis. So it will look like as shown in the following figure.

(x) Here for the given point the abscissa is 0 units and ordinate is 0 units.

The point is basically intersection of the coordinate axes. So it will look like as shown in the following figure.

#### Question 2:

Write the coordinates of each of the following points marked in the graph paper:

The following graph is given in the question with the marked points and we are asked to write down their coordinates.

The distance of point A from y-axis is 3 units and that of from x-axis is 1 units. Since A lies in the first quadrant, so its coordinates are.

The distance of point B from y-axis is 6 units and that of from x-axis is 0 units. Since B lies on x-axis, so its coordinates are

The distance of point C from y-axis is 0 units and that of from x-axis is 6 units. Since C lies on y-axis, so its coordinates are.

The distance of point D from y-axis is -3 units and that of from x-axis is 0 units. Since D lies on x-axis, so its coordinates are.

The distance of point E from y-axis is -4 units and that of from x-axis is 3 units. Since E lies in the second quadrant, so its coordinates are.

The distance of point F from y-axis is -2 units and that of from x-axis is -4 units. Since F lies in the third quadrant, so its coordinates are.

The distance of point G from y-axis is 0 units and that of from x-axis is -5 units. Since G lies on y-axis, so its coordinates are.

The distance of point H from y-axis is 3 units and that of from x-axis is -6 units. Since H lies in the fourth quadrant, so its coordinates are.

The distance of point P from y-axis is 7 units and that of from x-axis is -3 units. Since P lies in the fourth quadrant, so its coordinates are.

The distance of point Q from y-axis is 7 units and that of from x-axis is 6 units. Since Q lies in the first quadrant, so its coordinates are.

#### Question 1:

Mark the correct alternative in each of the following:

The point of intersect of the coordinate axes is

(a) ordinate

(b) abscissa

(d) origin

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).

#### Question 2:

The abscissa and ordinate of the origin are

(a) (0, 0)

(b) (1, 0)

(c) (0, 1)

(d) (1, 1)

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).

#### Question 3:

The measure of the angle between the coordinate axes is

(a) 0°

(b) 90°

(c) 180°

(d) 360°

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).

#### Question 4:

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

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

Thus the correct answer is (d).

#### Question 5:

Points (−4, 0) and (7, 0) lie

(a) on x-axis

(b) y-axis

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).

#### Question 6:

The ordinate of any point on x-axis is

(a) 0

(b) 1

(c) −1

(d) any number

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).

#### Question 7:

The abscissa of any point on y-axis is

(a) 0

(b) 1

(c) −1

(d) any number

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).

#### Question 8:

The abscissa of a point is positive in the

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

Thus the correct answer is (d).

#### Question 9:

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

As we know that

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).

#### 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

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).

#### 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

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).

#### Question 12:

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

(a) 4

(b) 3

(c) 5

(d) none of these

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).

#### Question 13:

The points (other than origin) for which abscissa is equal to the ordinate will lie in

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).

#### Question 14:

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

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).

#### Question 15:

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

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).

#### Question 16:

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

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).

#### Question 17:

A point whose abscissa and ordinate both are negative will lie in

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).

#### Question 18:

Points (2, –2), (3, –3), (4, –5), (–3, –4)
(d) do not lie in the same quadrant

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).

#### Question 19:

The points whose abscissa and ordinate have different signs will lie in

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).

#### Question 20:

Abscissa of a point is positive in

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).

#### 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

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

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

Thus, the quadrilateral OABC is a rectangle.

Hence, the correct answer is option (b).

#### 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)

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).

#### 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)

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).

#### 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

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).

#### 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)

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).

#### Question 26:

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

(a) 4

(b) 3

(c) 5

(d) 7

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)

#### 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

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:

$AB=OB-OA\phantom{\rule{0ex}{0ex}}=6-2\phantom{\rule{0ex}{0ex}}=4$
CD = 6

By using formula,

Thus the correct answer is (b).

#### 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

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).

#### Question 1:

Abscissa of all the points on y-axis is __________.

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). Thus, the abscissa of all points on the y-axis is 0.

Abscissa of all the points on y-axis is _____0_____.

#### Question 2:

Ordinate of all the points on x-axis is ___________.

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

​The co-ordinate of a point on the x-axis are of the form (x, 0). Thus, the ordinate of all points on the x-axis is 0.

Ordinate of all the points on x-axis is _____0_____.

#### Question 3:

Point (–7, 0) lies on the _________ direction of  _________ axis.

The given point is (–7, 0).

We know that, the co-ordinates of a point on the x-axis are of the form (x, 0).

If x > 0, then the point (x, 0) lies on the positive direction of the x-axis.

If x < 0, then the point (x, 0) lies on the negative direction of the x-axis.

The given point (–7, 0) is of the form (x, 0), where x < 0. Thus, the point (–7, 0) lies on the negative direction of the x-axis.

Point (–7, 0) lies on the __negative__ direction of  __x-__ axis.

#### Question 4:

Point (0, –3) lies on the _________ direction of __________ axis.

The given point is (0, –3).

We know that, the co-ordinates of a point on the y-axis are of the form (0, y).

If y > 0, then the point (0, y) lies on the positive direction of the y-axis.

If y < 0, then the point (0, y) lies on the negative direction of the y-axis.

The given point (0, –3) is of the form (0, y), where y < 0. Thus, the point (0, –3) lies on the negative direction of the y-axis.

Point (0, –3) lies on the __negative__ direction of  __y-__ axis.

#### Question 5:

The point at which the two coordinate axes meet is called the __________.

The point of intersection of the coordinate axes is called the origin.

The point at which the two coordinate axes meet is called the __origin__.

#### Question 6:

A point whose abscissa and ordinate both are negative lies in ____________.

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

A point whose abscissa and ordinate both are negative lies in __third quadrant__.

#### Question 7:

If y-coordinate of a point is zero, then it always lies on ____________ axis.

The y-coordinate of every point on x-axis is 0. So, the co-ordinates of any point on x-axis are of the form (x, 0).

If y-coordinate of a point is zero, then it always lies on __x-__ axis.

#### Question 8:

The points (–3, 2) and (2, –3) lie in __________ and __________ quadrants respectively.

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

In II quadrant: x < 0, y > 0

So, the point (–3, 2) lie in the second quadrant.

In IV quadrant: x > 0, y < 0

So, the point (2, –3) lie in the fourth quadrant.

The points (–3, 2) and (2, –3) lie in __second__ and __fourth__ quadrants respectively.

#### Question 9:

The point which lies on y-axis at a distance of 5 units in the negative direction of y-axis has the coordinates ________.

We know that, the co-ordinates of a point on the y-axis are of the form (0, y). The point (0, y) lies on the negative direction of the y-axis if y is negative.

The point lies on the y-axis so its x-coordinate is 0. Also, the point is at a distance of 5 units in the negative direction of y-axis so its y-coordinate is −5. Thus, the point is (0, −5).

The point which lies on y-axis at a distance of 5 units in the negative direction of y-axis has the coordinates __(0, −5)__.

#### Question 10:

If P(5, 1), Q(8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the point(s) on the x-axis are __________.

The given points are P(5, 1), Q(8, 0), R(0, 4), S(0, 5) and O(0, 0).  These points can be plotted on the graph paper as shown below.

It can be seen that, the points Q(8, 0) and O(0, 0) lie on the x-axis.

If P(5, 1), Q(8, 0), R(0, 4), S(0, 5) and O(0, 0) are plotted on the graph paper, then the point(s) on the x-axis are __Q(8, 0) and O(0, 0)__.

#### Question 11:

The coordinates of the point which lies on x and y-axes both are __________.

The point which lies on both x and y-axes is the point of intersection of x-axis and y-axis. The point of intersection of x-axis and y-axis is the origin. The coordinates of the origin are (0, 0).

The coordinates of the point which lies on x and y-axes both are ___(0, 0)___.

#### Question 12:

The coordinates of the point whose ordinate is –4 and which lies on y-axis, are ___________.

The ordinate of the point is –4.

So, y = –4

Now, the coordinates of a point on y-axis are of the form (0, y).

Thus, the coordinates of the point whose ordinate is –4 and which lies on y-axis are (0, –4).

The coordinates of the point whose ordinate is –4 and which lies on y-axis, are ___(0, –4)___.

#### Question 13:

The coordinates of point whose abscissa is 5 and which lies on x-axis, are _________.

The abscissa of the point is 5.

So, x = 5

Now, the coordinates of a point on x-axis are of the form (x, 0).

Thus, the coordinates of the point whose abscissa is 5 and which lies on x-axis are (5, 0).

The coordinates of point whose abscissa is 5 and which lies on x-axis, are ___(5, 0)___.

#### Question 14:

The image of the point (–3, –2) in x-axis lies in __________ quadrant.

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, –2) in the x-axis is (–3, 2).

In II quadrant: x < 0, y > 0

In the point (–3, 2), abscissa is negative and ordinate is positive. So, this point lies in the second quadrant.

The image of the point (–3, –2) in x-axis lies in __second__ quadrant.

#### Question 15:

If a > 0 and b < 0, then the image of (a, b) in y-axis lies in _________quadrant.

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).

If a > 0 and b < 0, then the point (a, b) lies in the fourth quadrant.

The coordinates of the image of point (a, b), where a > 0 and b < 0, in the y-axis are of the form (a, b), where a < 0 and b < 0.

Now, for a < 0 and b < 0, the point (a, b) lies in the third quadrant.

If a > 0 and b < 0, then the image of (a, b) in y-axis lies in __third__ quadrant.

#### Question 16:

The points O(0, 0), A(5, 0) and B(0, 5) are joined in order to form a/an __________ triangle.

The given points are O(0, 0), A(5, 0) and B(0, 5).  These points can be plotted on the graph paper as shown below.

Here, OA = 5 units and OB = 5 units

∴ OA = OB

Hence, the points O(0, 0), A(5, 0) and B(0, 5) form an isosceles right ∆OAB right angled at O.

The points O(0, 0), A(5, 0) and B(0, 5) are joined in order to form a/an __isosceles right__ triangle.

#### Question 17:

The points O(0, 0), A(7, 0), B(7, 4) and C(0, 4) form a ___________.

The given points are O(0, 0), A(7, 0), B(7, 4) and C(0, 4).  These points can be plotted on the graph paper as shown below.

From the figure, we have

OA = 7 units, AB = 4 units, BC = 7 units and OC = 4 units

OA = BC = 7 units and AB = OC = 4 cm

Thus, the quadrilateral OABC is a rectangle.

The points O(0, 0), A(7, 0), B(7, 4) and C(0, 4) form a ___rectangle___.

#### Question 18:

The points O(0, 0), A(6, 0) and B(0, 4) form a _________ triangle of area _________ sq. units.

The given points are O(0, 0), A(6, 0) and B(0, 4). These points can be plotted on the graph paper as shown below.

So, the points O(0, 0), A(6, 0) and B(0, 4) form right ∆OAB right angled at O.

From the figure, we have

OA = 6 units and OB = 4 units

∴ Area of ∆OAB = $\frac{1}{2}$ × OA × OB = $\frac{1}{2}$ × 6 × 4 = 12 square units

The points O(0, 0), A(6, 0) and B(0, 4) form a __right__ triangle of area ___12___ sq. units.

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