Question

Given the following endpoint (A) and midpoint (M), find the other endpoint (B).
M(2, 3)
A(0, -1)
1) (7, 4)
2) (3, 2)
3) (-1, 0)
4) (4, 7)

Answer 1

The midpoint of an interval is given by\[(a,b)=(\frac{x_1+x_2}{2})+(\frac{y_1+y_2}{2})\]Hence, we can identify,\[a=\frac{x_1+x_2}{2}\]and\[b=\frac{y_1+y_2}{2}\]In this case, we have,\[2=\frac{0+x}{2} \rightarrow x=4\]and\[3=\frac{-1+y}{2} \rightarrow y=7\]So the other point is (4,7).