Question

cd has a mid - point at m(16.5, 10.5). point c is at (20, 7). 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 $C(x_1,y_1)=(20,7)$ and $D(x_2,y_2)$. We know $M(16.5,10.5)$.

Step2: Solve for $x_2$

For the $x$ - coordinate of the mid - point: $\frac{x_1 + x_2}{2}=16.5$. Substitute $x_1 = 20$ into the equation: $\frac{20+x_2}{2}=16.5$. Multiply both sides by 2: $20 + x_2=33$. Then subtract 20 from both sides: $x_2=33 - 20=13$.

Step3: Solve for $y_2$

For the $y$ - coordinate of the mid - point: $\frac{y_1 + y_2}{2}=10.5$. Substitute $y_1 = 7$ into the equation: $\frac{7+y_2}{2}=10.5$. Multiply both sides by 2: $7 + y_2=21$. Then subtract 7 from both sides: $y_2=21 - 7 = 14$.

Answer:

$(13,14)$