## RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry VSAQS

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry VSAQS

**Other Exercises**

- RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry Ex 6.1
- RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry Ex 6.2
- RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry Ex 6.3
- RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry Ex 6.4
- RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry Ex 6.5
- RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry VSAQS
- RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry MCQS

**Answer each of the following questions either in one word or one sentence or as per requirement of the questions :**

**Question 1.**

Write the distance between the points A (10 cosθ, 0) and B (0, 10 sinθ).

**Solution:**

Distance between the points A (10 cosθ, 0) and B (0, 10 sinθ)

**Question 2.**

Write the perimeter of the triangle formed by the points O (0, 0), A (a, 0), and B (0, b).

**Solution:**

The vertices of a ∆OAB, O (0, 0), A (a, 0), and B (0, b)

Now length of OA

**Question 3.**

Write the ratio in which the line segment joining points (2, 3) and (3, -2) is divided by x-axis.

**Solution:**

The required point is on x-axis

Its ordinate will be 0

Let the point be (x, 0) and let this point divides the join of the points (2, 3) and (3, -2) in the ratio m : n

**Question 4.**

What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°) ?

**Solution:**

Distance between the given points

**Question 5.**

If A (-1, 3), B (1, -1) and C (5, 1) are the vertices of a triangle ABC, what is the length of the median through vertex A ?

**Solution:**

The vertices of ∆ABC are A (-1, 3), B (1, -1) and C (5, 1)

Let AD be the median

**Question 6.**

If the distance between points (x, 0) and (0, 3) is 5, what are the value of x ?

**Solution:**

Distance between (x, 0) and (0, 3) = 5

**Question 7.**

What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4) ?

**Solution:**

The vertices of the triangle OAB are O (0, 0), A (6, 0) and B (0, 4)

**Question 8.**

Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.

**Solution:**

Let the coordinates of the required point be (x, y), then

**Question 9.**

If the centroid of the triangle formed by points P (a, b), Q (b, c) and R (c, a) is at the origin, what is the value of a + b + c ?

**Solution:**

Vertices of ∆PQR are P (a, b), Q (b, c) and R (c, a) and its centroid = O (0, 0)

**Question 10.**

**Solution:**

**Question 11.**

Write the coordinates of a point on x- axis which is equidistant from the points (-3, 4) and (2, 5).

**Solution:**

The point is on x-axis

Its ordinates of the point P is (x, 0)

P is equidistant from A (-3, 4) and B (2, 5)

**Question 12.**

If the mid-point of the segment joining A (x, y + 1) and B (x + 1, y + 2) is C (\(\frac { 3 }{ 2 }\) , \(\frac { 5 }{ 2 }\)) find x, y.

**Solution:**

C (\(\frac { 3 }{ 2 }\) , \(\frac { 5 }{ 2 }\)) is mid point of the line segment

**Question 13.**

Two vertices of a triangle have co-ordinates (-8, 7) and (9, 4). If the centroid of the triangle is at the origin, what are the co-ordinates of the third vertex ?

**Solution:**

Two vertices of a triangle are (-8, 7) and (9, 4)

Let the third vertex be (x, y)

Centroid of the triangle is (0, 0)

**Question 14.**

Write the coordinates the reflections of points (3, 5) in x and y-axes.

**Solution:**

Reflection of P (3, 5) in x-axis is will be (3, -5)

and reflection of P in y-axis will be (-3, 5)

**Question 15.**

If points Q and R reflections of point P (-3, 4) in X and Y axes respectively, what is QR ?

**Solution:**

Reflection of point P (-3, 4) in X-axis will be Q with coordinates Q (-3, -4) and reflection in Y-axis will be R (3, 4)

**Question 16.**

Write the formula for the area of the triangle having its vertices at (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}).

**Solution:**

**Question 17.**

Write the condition of collinearity of points (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}).

**Solution:**

Three points (x_{1}, y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3}). are said to be collinear if the area of the triangle formed by these point = 0 i.e.,

**Question 18.**

Find the values of x for which the distance between the point P (2, -3) and Q (x, 5) is 10.

**Solution:**

Distance between P (2, -3) and Q (x, 5) = 10

**Question 19.**

Write the ratio in which the line segment joining the points A (3, -6) and B (5, 3) is divided by X-axis.

**Solution:**

The point lies on x-axis

Its ordinate will be = 0

Let the point P (x, 0) divides the line segment joining the points A (3, -6) and B (5, 3) in the ratio m : n.

**Question 20.**

Find the distance between the points (\(\frac { -8 }{ 5 }\) , 2) and (\(\frac { 2 }{ 5 }\) , 2). **(C.B.S.E. 2009)**

**Solution:**

**Question 21.**

Find the value of a so that the point (3, a) lies on the line represented by 2x – 3y + 5 = 0. **(C.B.S.E. 2009)**

**Solution:**

**Question 22.**

What is the distance between the points A (c, 0) and B (0, – c) ? **[CBSE 2010]**

**Solution:**

**Question 23.**

If P (2, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y. **[CBSE 2010]**

**Solution:**

P (2, 6) is the mid-point of the line segment A (6, 5) and b (4, y)

**Question 24.**

If the distance between the points (3, 0) and (0, y) is 5 units and y is positive, then what is the value of y ? **[CBSE 2010]**

**Solution:**

Distance between (3, 0) and (0, y) is 5 units

**Question 25.**

If P (x, 6) is the mid-point of the line segment joining A (6, 5) and B (4, y), find y. **[CBSE 2010]**

**Solution:**

P (x, 6) is the mid-point of the line segment joining the points A (6, 5), B (4, y)

**Question 26.**

If P (2, p) is the mid-point of the line segment joining the points A (6, -5) and B (-2, 11), find the value of p. **[CBSE 2010]**

**Solution:**

P (2, p) is the mid-point of the line segment joining the points A (6, -5) and B (-2, 11)

**Question 27.**

If A (1, 2), B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D. **[CBSE 2010]**

**Solution:**

vertices of a parallelogram Let co-ordinates of D be (x, y)

Diagonals AC and BD bisect each other at O

Co-ordinates of O will be

**Question 28.**

What is the distance between the points A (sinθ – cosθ, 0) and B (0, sinθ + cosθ)? **[CBSE 2015]**

**Solution:**

**Question 29.**

What are the coordinates of the point where the perpendicular bisector of the line segment joining the points A (1, 5) and B (4, 6) cuts the y-axis?

**Solution:**

Firstly, we plot the points of the line segment on the paper and join them.

Now, we draw a straight line on paper passes through the mid-point P.

We see that the perpendicular bisector cuts the y-axis at the point (0, 13).

Hence, the required point is (0, 13).

**Question 30.**

Find the area of the triangle with vertices (a, b + c), (b, c + a) and (c, a + b).

**Solution:**

**Question 31.**

If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then find a : b.

**Solution:**

=> 2a = b

Hence, the required relation is 2a = b

**Question 32.**

Find the coordinates of the point which is equidistant from the three vertices A (2x, 0), O (0, 0) and B (0, 2y) of ∆AOB.

**Solution:**

Let the coordinate of the point which is equidistant from the three vertices O (0, 0), A (0, 2y) and B (2x, 0) is P (h, k).

**Question 33.**

If the distance between the points (4, k), and (1, 0) is 5, then what can be the possible value of k? **[CBSE 2017]**

**Solution:**

Let the points x (4, k) and y (1, 0)

It is given that the distance xy is 5 units.

By using the distance formula,

Hope given RD Sharma Class 10 Solutions Chapter 6 Co-ordinate Geometry VSAQS are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.