Question

The midpoint of JK is point L at (–1, 8). One endpoint is J(4, –15). Which equations can be solved to determine the coordinates of the other endpoint, K? Check all that apply.  = –1  = 4 –15 + y1 = 4 –15 + y1 = 16  = x1 = y1

Answer 1

Given two endpoints: $(x_1,\ y_1)$ and $(x_2,\ y_2)$, the midpoint of the two endpoints $(x_m,\ y_m)$ is given by
$(x_m,\ y_m)=\left( \frac{x_1+x_2}{2} ,\ \frac{y_1+y_2}{2}\right)$

Thus, given the midpoint L(-1, 8) and one endpoint J(4, -15). The second endpont is given by
$(-1,\ 8)=\left( \frac{x_1+4}{2} ,\ \frac{y_1+(-15)}{2}\right)$
i.e.
$\frac{x_1+4}{2} =-1 \\ \\ x_1+4=-2 \\ \\ x_1=-2-4=-6$
and
$\frac{y_1+(-15)}{2}=8 \\ \\ y_1-15=16 \\ \\ y_1=16+15=31$

Answer 2

A and D

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