Question

bc has a midpoint at m(4, 4). point b is at (6, 0). find the coordinates of point c. write the coordinates as decimals or integers. c = ( ) ( )

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 $B(6,0)$ be $(x_1,y_1)$ and $C(x,y)$ be $(x_2,y_2)$, and $M(4,4)$.

Step2: Solve for x - coordinate of C

We have $\frac{6 + x}{2}=4$. Multiply both sides by 2: $6 + x=8$. Then subtract 6 from both sides: $x=8 - 6=2$.

Step3: Solve for y - coordinate of C

We have $\frac{0 + y}{2}=4$. Multiply both sides by 2: $0 + y = 8$. So $y = 8$.

Answer:

$(2,8)$