Question

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

Answer 1

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).