Question

the midpoint of cd is m = (1, 6). one endpoint is c = (-5, 4). find the coordinates of the other endpoint, d.

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 $C=(-5,4)=(x_1,y_1)$ and $D=(x_2,y_2)$, and $M=(1,6)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=1$. Substitute $x_1=-5$ into the equation: $\frac{-5 + x_2}{2}=1$. Multiply both sides by 2: $-5 + x_2=2$. Then add 5 to both sides: $x_2=2 + 5=7$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=6$. Substitute $y_1 = 4$ into the equation: $\frac{4 + y_2}{2}=6$. Multiply both sides by 2: $4 + y_2=12$. Then subtract 4 from both sides: $y_2=12 - 4 = 8$.

Answer:

$(7,8)$