Question

the midpoint of $overline{bc}$ is $m(4,8)$. one endpoint is $c(1,8)$. find the coordinates of the other endpoint $b$. write the coordinates as decimals or integers. $b = ( square, square )$

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 $B=(x,y)$ and $C=(1,8)$, and $M=(4,8)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 1}{2}=4$. Cross - multiply: $x + 1=8$. Then $x=8 - 1=7$.

Step3: Solve for y - coordinate

We know that $\frac{y + 8}{2}=8$. Cross - multiply: $y+8 = 16$. Then $y=16 - 8=8$.

Answer:

$(7,8)$