Question

1. find the coordinates of r if q(-1, 3) is the midpoint of pr and p has coordinates of (5, 6).

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 $P=(x,y)=(5,6)$ and $Q=(-1,3)$ be the mid - point of $\overline{PR}$, and $R=(x_R,y_R)$. Then $-1=\frac{5 + x_R}{2}$ and $3=\frac{6 + y_R}{2}$.

Step2: Solve for $x_R$

Cross - multiply the $x$ - coordinate equation: $-1=\frac{5 + x_R}{2}$ gives $-2 = 5+x_R$. Then $x_R=-2 - 5=-7$.

Step3: Solve for $y_R$

Cross - multiply the $y$ - coordinate equation: $3=\frac{6 + y_R}{2}$ gives $6 = 6+y_R$. Then $y_R=0$.

Answer:

$(-7,0)$