Question

the midpoint of cd is m(3, -8). one endpoint is d(2, -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 $D=(2,-6)$ and $M=(3,-8)$.

Step2: Solve for x - coordinate of C

We know that $\frac{x + 2}{2}=3$. Cross - multiply: $x + 2=6$. Then subtract 2 from both sides: $x=6 - 2=4$.

Step3: Solve for y - coordinate of C

We know that $\frac{y+( - 6)}{2}=-8$. Cross - multiply: $y-6=-16$. Then add 6 to both sides: $y=-16 + 6=-10$.

Answer:

$(4,-10)$