Question

Segment DG has endpoints D(-7,-4) and G(8,1). Find the coordinates of J such that the ratio of DJ:JG is 2:3

Answer 1

Given:

DG has endpoints D(-7,-4) and G(8,1).

DJ:JG = 2:3

To find:

The coordinates of J.

Solution:

We have,

DJ:JG = 2:3

It means, point J divides the segment DG is 2:3.

Section formula: If a point divides a lines segment with end point $(x_1,y_1)$ and $(x_2,y_2)$ in m:n, then coordinates of point are

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

Using section formula, the coordinate of J are

$J=\left(\dfrac{2(8)+3(-7)}{2+3},\dfrac{2(1)+3(-4)}{2+3}\right)$

$J=\left(\dfrac{16-21}{5},\dfrac{2-12}{5}\right)$

$J=\left(\dfrac{-5}{5},\dfrac{-10}{5}\right)$

$J=\left(-1,-2\right)$

Therefore, the coordinates of J are (-1,-2).