Question

the midpoint of cd is m(2, 6). one endpoint is d(4, 6). find the coordinates of the other endpoint 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 $C=(x,y)$ and $D=(4,6)$ and $M=(2,6)$.

Step2: Solve for x - coordinate of C

We know that $\frac{x + 4}{2}=2$. Multiply both sides by 2: $x + 4=4$. Then subtract 4 from both sides: $x=0$.

Step3: Solve for y - coordinate of C

We know that $\frac{y + 6}{2}=6$. Multiply both sides by 2: $y+6 = 12$. Then subtract 6 from both sides: $y = 6$.

Answer:

$(0,6)$