Answer
a) $R(-8,9)$
b) 17.9
Work Step by Step
a) Use the midpoint formula:
$M_x=\frac{x_1+x_2}{2}$
$-4=\frac{x_R+0}{2}$
$-4\times2=\frac{x_R+0}{2}\times2$
$-8=x_R$
$M_y=\frac{y_1+y_2}{2}$
$1=\frac{y_R+(-7)}{2}$
$1\times2=\frac{y_R+(-7)}{2}\times2$
$2=y_R-7$
$2+7=y_R-7+7$
$9=y_R$
b) Use the distance formula:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d=\sqrt{(0-(-8))^2+(-7-9)^2}$
$d=\sqrt{(8)^2+(-16)^2}$
$d=\sqrt{64+256}$
$d=\sqrt{320}$
$d\approx17.9$
