Question

Find the coordinates of the point which divides the line segment joining the points (1, –2, 3) and (3, 4, –5) internally in the ratio 2 : 3.

Options

• `(9/5, 2/5, 1/5)`

• `(9/5, 2/5, (-1)/5)`

• `(9/5, (-2)/5, 1/5)`

• `((-9)/5, (-2)/5, 1/5)`

Answer 1

`(9/5, 2/5, (-1)/5)`

Explanation:

Let (x, y, z) be the point which divides line segment joining A(1, –2, 3) and B(3, 4, –5) internally in the ratio 2 : 3.

Therefore

x = `(2(3) + 3(1))/(2 + 3) = 9/5`

y = `(2(4) + 3(-2))/(2 + 3) = 2/5`

z = `(2(-5) + 3(3))/(2 + 3) = (-1)/5`

Thus, the required point is `(9/5, 2/5, (-1)/5)`