Question

the midpoint of rs is m(-3, 3). one endpoint is r(0, 1). find the coordinates of the other endpoint s. write the coordinates as decimals or integers. s = ( )

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 $R(x_1,y_1)=(0,1)$ and $S(x_2,y_2)$. The mid - point $M(-3,3)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-3$. Substitute $x_1 = 0$ into the equation: $\frac{0 + x_2}{2}=-3$. Multiply both sides by 2: $0+x_2=-6$. So $x_2=-6$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=3$. Substitute $y_1 = 1$ into the equation: $\frac{1 + y_2}{2}=3$. Multiply both sides by 2: $1 + y_2=6$. Subtract 1 from both sides: $y_2=5$.

Answer:

$(-6,5)$