Question

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.)

Answer 1

`(2x_m - x_1 , 2y_m -y_1)`

Explanation:

Let
`(x,y)` be the unknown endpoint.

Denote the one endpoint by
`(x_1, y_1)` and the midpoint by
`(x_m, y_m)`.

As the midpoint divides the segment in
`1:1` ratio, so, from section formula

`x_m=(x_1+x)/(2) \Rightarrow x=2x_m-x_1.`

and
`y_m=(y_1+x)/(2) \Rightarrow y=2x_m-y_1.`

Hence, the coordinate of the other endpoint is
`(x,y)=(2x_m - x_1 , 2y_m -y_1)`.