P is the midpoint of the line segment AB. The coordinates of P are (5,-6). The coordinates of A are (-1,10). How do you find the coordinates of B?

1 Answer
Nov 19, 2015

B=(x_2, y_2)=(11, -22)

Explanation:

If one end-point(x_1, y_1) and mid-point(a, b) of a line-segment is known, then we can use mid-point formula to find the second end-point#(x_2, y_2).

How to use midpoint formula to find an endpoint?

(x_2, y_2)=(2a-x_1, 2b-y_1)

Here,
(x_1, y_1)=(-1, 10)
and
(a, b)=(5, -6)

So,
(x_2, y_2)=(2color(red)((5)) -color(red)((-1)), 2color(red)((-6))-color(red)10)
(x_2, y_2)=(10+1, -12-10)
(x_2, y_2)=(11, -22)