Question

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

guided practice

1. using the diagram to the left, if line n bisects $overline{qr}$, find qp.

3x + 5 5x - 19
q p r

Explanation:

Step1: Recall mid - point formula

Let $P(x_1,y_1)=(5,6)$ and $Q(x_m,y_m)=(-1,3)$, $R(x_2,y_2)$. The mid - point formula is $x_m=\frac{x_1 + x_2}{2}$ and $y_m=\frac{y_1 + y_2}{2}$.

Step2: Solve for $x_2$

$-1=\frac{5 + x_2}{2}$, then $-2 = 5+x_2$, $x_2=-7$.

Step3: Solve for $y_2$

$3=\frac{6 + y_2}{2}$, then $6 = 6+y_2$, $y_2 = 0$.

Answer:

$(-7,0)$