Question

1. b is the midpoint of $overline{ac}$ and e is the midpoint of $overline{bd}$. if $a(-9, -4)$, $c(-1, 6)$, and $e(-4, -3)$, find the coordinates of d.

Explanation:

Step1: Find coordinates of B

Use mid - point formula $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. For points $A(-9,-4)$ and $C(-1,6)$, $x_B=\frac{-9+( - 1)}{2}=\frac{-9 - 1}{2}=-5$, $y_B=\frac{-4 + 6}{2}=1$. So $B(-5,1)$.

Step2: Let coordinates of D be $(x,y)$

Since E is mid - point of $\overline{BD}$ and $E(-4,-3)$, $B(-5,1)$. Using mid - point formula again, for x - coordinate: $\frac{-5+x}{2}=-4$. Solve for x: $-5+x=-8$, $x=-8 + 5=-3$. For y - coordinate: $\frac{1+y}{2}=-3$. Solve for y: $1+y=-6$, $y=-6 - 1=-7$.

Answer:

$D(-3,-7)$