Question

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?

Answer 1

`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)`