Question

distance, midpoint, and slope formula practice
given the midpoint and one endpoint of a line segment, find the other endpoint.
endpoint: (-3,2), midpoint: (9,0)
endpoint: ( )

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 the known endpoint be $(x_1,y_1)=(-3,2)$ and the mid - point be $(x_m,y_m)=(9,0)$. Let the unknown endpoint be $(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $9=\frac{-3 + x_2}{2}$. Multiply both sides by 2: $18=-3 + x_2$. Then add 3 to both sides: $x_2=18 + 3=21$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $0=\frac{2 + y_2}{2}$. Multiply both sides by 2: $0 = 2+y_2$. Then subtract 2 from both sides: $y_2=-2$.

Answer:

$(21,-2)$