Question

a) find the coordinates of d if e(-6, 4) is the midpoint of $overline{df}$ and f has coordinates (-5, -3).

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of $D$ be $(x,y)$ and $F(-5,-3)$ and $E(-6,4)$.

Step2: Find the x - coordinate of D

We know that $\frac{x+( - 5)}{2}=-6$. Multiply both sides by 2: $x - 5=-12$. Then add 5 to both sides: $x=-12 + 5=-7$.

Step3: Find the y - coordinate of D

We know that $\frac{y+( - 3)}{2}=4$. Multiply both sides by 2: $y-3 = 8$. Then add 3 to both sides: $y=8 + 3 = 11$.

Answer:

$(-7,11)$