Question

What are the coordinates of the point on the directed line segment from (-2, -5)(−2,−5) to (7, 10)(7,10) that partitions the segment into a ratio of 2 to 1?

Answer 1

Given:

The directed line segment from (-2, -5) to (7, 10).

A point partitions the segment into a ratio of 2 to 1.

To find:

The coordinates of that point.

Solution:

Section formula: If a point divides a line segment in m:n, then the coordinates of that point are

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

The point divides the line segment from (-2, -5) to (7, 10) in 2:1.

Using section formula, we get

$Point=\left(\dfrac{2(7)+1(-2)}{2+1},\dfrac{2(10)+1(-5)}{2+1}\right)$

$Point=\left(\dfrac{14-2}{3},\dfrac{20-5}{3}\right)$

$Point=\left(\dfrac{12}{3},\dfrac{15}{3}\right)$

$Point=\left(4,5\right)$

Therefore, the coordinates of the partition point are (4,5).