Question

A segment has midpoint at (2,-4) and an endpoint at (5,-9). What are the coordinates of the other endpoint?

Answer 1

Answer:

The coordinates of the other endpoint are (-1,1).

Explanation:

Mid point = (2,-4)

One endpoint = (5,-9)

We need to find the coordinates of the other mid points. Let it is (x₂,y₂). Using the mid point formula to find it.

$\text{Mid-points}(x_m,y_m)=(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})$

We have, $x_m=2, y_m=-4, x_1=5, y_1=-9$

$\text{Mid-points}(2,-4)=(\dfrac{5+x_2}{2}, \dfrac{(-9)+y_2}{2})\\\\\dfrac{5+x_2}{2}=2\ \text{and}\ \dfrac{y_2-9}{2}=-4\\\\5+x_2=4\ \text{and}\ y_2-9=-8\\\\x_2=-1\ \text{and}\ y_2=1$

So, the coordinates of the other endpoint are (-1,1).