If P (4,-1) is the midpoint of the segment AB, where A (2, 5), what is B?
B is (6, -7)
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
This means that the x coordinate of B will be:
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
That means that the y coordinate of B is 6 less than the y coordinate of P.
This gives us B(6, -7).