Question

cd has a mid - point at m(10, 4). point c is at (2, 18). find the coordinates of point d. write the coordinates as decimals or integers. 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 $C(x_1,y_1)=(2,18)$ and $D(x_2,y_2)$, and $M(10,4)$.

Step2: Solve for the x - coordinate of D

We know that $\frac{x_1 + x_2}{2}=10$. Substitute $x_1 = 2$ into the equation: $\frac{2+x_2}{2}=10$. Multiply both sides by 2: $2+x_2 = 20$. Then subtract 2 from both sides: $x_2=18$.

Step3: Solve for the y - coordinate of D

We know that $\frac{y_1 + y_2}{2}=4$. Substitute $y_1 = 18$ into the equation: $\frac{18 + y_2}{2}=4$. Multiply both sides by 2: $18+y_2 = 8$. Then subtract 18 from both sides: $y_2=-10$.

Answer:

$(18,-10)$