RD Sharma 2020 2021 Solutions for Class 9 Maths Chapter 8 - Coordinate Geometry

Answer:

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.

Answer:

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.

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).

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).

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).

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).

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).

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).

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).

Answer:

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

Thus the correct answer is (d).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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 < 0 

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).

 

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).

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).

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).

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).

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).

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).

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).

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)

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:

$$\begin{gathered} AB=OB-OA \\ =6-2 \\ =4 \end{gathered}$$
CD = 6

By using formula,

$$\begin{gathered} ∆ABC=\frac{1}{2}\times AB\times CD \\ =\frac{1}{2}\times 4\times 6 \\ =12 sq units \end{gathered}$$

Thus the correct answer is (b).

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).

Answer:

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_____.

Answer:

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_____.

Answer:

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.

Answer:

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.

Answer:

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__.

Answer:

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__.

Answer:

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.

Answer:

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.

Answer:

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)__.

Answer:

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)__.

Answer:

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)___.

Answer:

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)___.

Answer:

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)___.

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, –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.

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).

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.

Answer:

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.

Answer:

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

In quadrilateral OABC,

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___.

Answer:

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.