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

Nov 14, 2015

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 $\left(4 - 2 = 2\right)$.

This means that the x coordinate of B will be:
$x \left(P\right) + 2 = x \left(B\right)$
$4 + 2 = x \left(B\right)$
$x \left(B\right) = 6$
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 $y \text{coordinate of P" - y "coordinate of A}$:
$- 1 - 5 = - 6$

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

This gives us B(6, -7).