Question

distance, midpoint, and slope formula practice
given the midpoint and one endpoint of a line segment, find the other endpoint.
endpoint: (7, -9), midpoint: (8, -4)
endpoint: ( )

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 the known endpoint be $(x_1,y_1)=(7,-9)$ and the mid - point be $(M_x,M_y)=(8,-4)$, and the unknown endpoint be $(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $M_x=\frac{x_1 + x_2}{2}$. Substituting the values, we have $8=\frac{7 + x_2}{2}$. Cross - multiply: $8\times2=7 + x_2$, so $16=7 + x_2$. Then $x_2=16 - 7=9$.

Step3: Solve for $y_2$

We know that $M_y=\frac{y_1 + y_2}{2}$. Substituting the values, we have $-4=\frac{-9 + y_2}{2}$. Cross - multiply: $-4\times2=-9 + y_2$, so $-8=-9 + y_2$. Then $y_2=-8 + 9 = 1$.

Answer:

$(9,1)$