The midpoint of segment AB is (-7, 10) and endpoint A is located at (3, -1). Find the other endpoint B. Show all work.

Mathematics

1 answer:

dusya [7]3 years ago

6 0

Answer:

$B(-17,21)$

Step-by-step explanation:

The midpoint of two points is the average of the x coordinates and the average of the y coordinates.

Given

A(3, -1)

and we let the other end point B be B(x,y)

and midpoint is (-7,10)

So, the average of 3 and x is -7, and

the average of -1 and y is 10

We can solve for x first:

$\frac{3+x}{2}=-7\\3+x=2*-7\\3+x=-14\\x=-14-3\\x=-17$

and now solving for y:

$\frac{-1+y}{2}=10\\-1+y=2*10\\-1+y=20\\y=20+1\\y=21$

So, the other point B is:

$B(-17,21)$

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