Question

The midpoint of ST is M=(-2, 1). One endpoint is S=(3, -4).Find the coordinates of the other endpoint, T.

Answer 1

The midpoint of ST is M(-2, 1)

One endpoint is S(3, -4)

Recall that the midpoint formula is given by

$(x_m,y_m)=(\frac{x_1+x_2}{2},\; \frac{y_1+y_2}{2}_{})$

Let us substitute the given points into the above formula

$\begin{gathered} (-2_{},1_{})=(\frac{3_{}+x_2}{2},\; \frac{-4_{}+y_2}{2}_{}) \\ -2_{}=\frac{3_{}+x_2}{2},\; \; 1=\frac{-4_{}+y_2}{2}_{} \\ -2_{}\cdot2=3_{}+x_2,\; \; 1\cdot2=-4_{}+y_2 \\ -4=3_{}+x_2,\; \; 2=-4_{}+y_2 \\ -4-3=x_2,\; \; 2+4=_{}y_2 \\ -7=x_2,\; \; 6=_{}y_2 \\ x_2=-7,\; \; y_2=6 \end{gathered}$

Therefore, the other endpoint is T(-7, 6)