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,

Coordinate Geometry Exercise 14.4

 

  1. 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,

Coordinate Geometry Exercise 14.4

To find y2,

Coordinate Geometry Exercise 14.4

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

 

  1. 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,

Coordinate Geometry Exercise 14.4

To find y2,

Coordinate Geometry Exercise 14.4

Therefore, m:n = 2:7  and k = 6.

 

  1. 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).

Coordinate Geometry Exercise 14.4

 

  1. 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.

Coordinate Geometry Exercise 14.4

We know, diagonals of the parallelogram are equal.

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

Then,

Coordinate Geometry Exercise 14.4

Also

 

Coordinate Geometry Exercise 14.4

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