**Coordinate Geometry Exercise 14.4 – Questions:**

**In what ratio does the point (-2, 3) divide the line segment joining the points (-3, 5) and (4, -9)?****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.****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.****Find the coordinates of the midpoint of the line joining the points (-3, 10) and (6, -8).****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:**

**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: (x_{1}, y_{1}) = (-2, 3), (x_{2}, y_{2}) = (4, -9) and (x , y) = (-2, 3)

By section formula,

**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: (x_{1}, y_{1}) = (-2, 7) , m:n = 3:2 and (x , y) = (1, 1) . We have to find (x_{2}, y_{2}).

By section formula,

To find x_{2},

To find y_{2},

Therefore, (x_{2}, y_{2}) = (3, -3) .Hence B(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), (x_{1}, y_{1}) = (-3, 10) and (x_{2}, y_{2}) = (6, -8)

By section formula,

To find m:n,

To find y_{2},

Therefore, m:n = 2:7 and k = 6.

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

Solution:

Given, (x_{1}, y_{1}) = (-3, 10) and (x_{2}, y_{2}) = (6, -8).

**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