Question

qr has a mid - point at m(-6, 1). point q is at (-6, 3). 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 $Q(x_1,y_1)=(-6,3)$ and $R(x_2,y_2)$. The mid - point $M(-6,1)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-6$. Substitute $x_1=-6$ into the equation: $\frac{-6 + x_2}{2}=-6$. Multiply both sides by 2: $-6 + x_2=-12$. Add 6 to both sides: $x_2=-6$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=1$. Substitute $y_1 = 3$ into the equation: $\frac{3 + y_2}{2}=1$. Multiply both sides by 2: $3 + y_2=2$. Subtract 3 from both sides: $y_2=-1$.

Answer:

$(-6,-1)$