Question

the mid - point m of $overline{qr}$ has coordinates (-7, -6). point q has coordinates (-6, -9). find the coordinates of point r. write the coordinates as decimals or integers. r=( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $Q(x_1,y_1)=(-6,-9)$ and $R(x_2,y_2)=(x,y)$, and $M(-7,-6)$.

Step2: Solve for the x - coordinate of R

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting the values, we have $\frac{-6 + x}{2}=-7$. Multiply both sides by 2: $-6 + x=-14$. Then add 6 to both sides: $x=-14 + 6=-8$.

Step3: Solve for the y - coordinate of R

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting the values, we have $\frac{-9 + y}{2}=-6$. Multiply both sides by 2: $-9 + y=-12$. Then add 9 to both sides: $y=-12 + 9=-3$.

Answer:

$R=(-8,-3)$