Coordinate Geometry Exercise 14.4 – Class 10

Coordinate Geometry Exercise 14.4 – Questions:

1. In what ratio does the point (-2, 3) divide the line segment joining the points (-3, 5) and (4, -9)?
2. In the point C(1, 1) divides the line segment joining A(-2, 7) and B in the ratio 3:2, find the coordinates of B.
3. Find the ratio in which the point (-1, k) divides the line joining the points (-3, 10) and (6, -8) and find the value of k.
4. Find the coordinates of the midpoint of the line joining the points (-3, 10) and (6, -8).
5. Three consecutive vertices of a parallelogram are A(1, 2), B(2, 3) and C(8, 5). Find the fourth vertex. [Hint: diagonals of a parallelogram bisect each other]

Coordinate Geometry Exercise 14.4 – Solutions:

1. In what ratio does the point (-2, 3) divide the line segment joining the points (-3, 5) and (4, -9)?

Solution:

Let the required ratio be m:n

Given: (x₁, y₁­) = (-2, 3), (x₂, y₂) = (4, -9) and (x , y) = (-2, 3)

By section formula,

 

2. In the point C(1, 1) divides the line segment joining A(-2, 7) and B in the ratio 3:2, find the coordinates of B.

Solution:

Let the required ratio be m:n

Given: (x₁, y₁­) = (-2, 7) , m:n = 3:2 and (x , y) = (1, 1) . We have to find (x₂, y₂).

By section formula,

To find x₂,

To find y₂,

Therefore, (x₂, y₂) = (3, -3) .Hence B(3, -3).

 

3. Find the ratio in which the point (-1, k) divides the line joining the points (-3, 10) and (6, -8) and find the value of k.

Solution:

Given, (x, y)= (-1, k), (x₁, y₁) = (-3, 10) and (x₂, y₂) = (6, -8)

By section formula,

To find m:n,

To find y₂,

Therefore, m:n = 2:7  and k = 6.

 

4. Find the coordinates of the midpoint of the line joining the points (-3, 10) and (6, -8).

Solution:

Given, (x₁, y₁) = (-3, 10) and (x₂, y₂) = (6, -8).

 

5. Three consecutive vertices of a parallelogram are A(1, 2), B(2, 3) and C(8, 5). Find the fourth vertex. [Hint: diagonals of a parallelogram bisect each other]

Solution:

Given, A(1, 2), B(2, 3) and C(8, 5)

Diagonal of a parallelogram bisect each other. Therefore, diagonal of the parallelogram is the midpoint.

We know, diagonals of the parallelogram are equal.

Therefore, we have, (⁹/₂, ⁷/₂) = (^2+x/₂, ^3+y/₂)

Then,

Also