If P (4,-1) is the midpoint of the segment AB, where A (2, 5), what is B?

1 Answer
Nov 14, 2015

Answer:

B is (6, -7)

Explanation:

First, we have to see how the x and y coordinates has changed between A and P.

A(2, 5) , P(4, -1)

Let's have a look at the x coordinates.
From A to P, the x coordinate has moved 2 steps in positive direction #(4-2 = 2)#.

This means that the x coordinate of B will be:
#x(P) + 2 = x(B)#
#4 + 2 = x(B)#
#x(B) = 6#
Where x(P) is the x coordinate of P, and x(B) is the x coordinate of B.

Let's do the same thing with the y-coordinates.
The y coordinate has moved 6 steps in negative direction (or -6 steps). You can calculate this by taking the #y "coordinate of P" - y "coordinate of A"#:
#-1 - 5 = -6#

That means that the y coordinate of B is 6 less than the y coordinate of P.
#y(P) - 6 = y(B)#
#-1 -6 = y(B)#
#y(B) = -7#

This gives us B(6, -7).