Question

the midpoint m of cd has coordinates (16.5, 13.5). point d has coordinates (20, 14). find the coordinates of point 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 the coordinates of point $C$ be $(x,y)$, point $M=(16.5,13.5)$ and point $D=(20,14)$. Then $\frac{x + 20}{2}=16.5$ and $\frac{y + 14}{2}=13.5$.

Step2: Solve for $x$

Solve the equation $\frac{x + 20}{2}=16.5$. Multiply both sides by 2: $x + 20=16.5\times2=33$. Then subtract 20 from both sides: $x=33 - 20=13$.

Step3: Solve for $y$

Solve the equation $\frac{y + 14}{2}=13.5$. Multiply both sides by 2: $y + 14=13.5\times2 = 27$. Then subtract 14 from both sides: $y=27-14 = 13$.

Answer:

$(13,13)$