The midpoint of segment AB has the coordinates M(-4,2). If the coordinates of endpoint A are (-6, -7), find the coordinates of endpoint B.

Question

asked Sep 16, 2021 78.6k views

1 Answer

Kiminoa · Answer 1 · 2021-09-20T10:07:36+0000

Given:

The midpoint of segment AB has the coordinates M(-4,2).

The coordinates of endpoint A are (-6, -7).

To find:

The coordinates of B.

Solution:

Let the coordinates of point B are (a,b).

Formula for midpoint:

$Midpoint=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right)$

The midpoint of segment AB has the coordinates M(-4,2), so by using the above formula we get

$M=\left((-6+a)/(2),(-7+b)/(2)\right)$

$(-4,2)=\left((-6+a)/(2),(-7+b)/(2)\right)$

On comparing both sides, we get

(-6+a)/(2)=-4

-6+a=-8

a=-8+6

a=-2

And,

(-7+b)/(2)=2

-7+b=4

b=4+7

b=11

Therefore, the coordinates of point B are (-2,11).