Question

cd has a midpoint at m(48.5, 61). point d is at (3, 88). 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 $(x,y)$ and point $D(3,88)$ and mid - point $M(48.5,61)$.

Step2: Solve for $x$

We know that $\frac{x + 3}{2}=48.5$. Multiply both sides by 2: $x + 3=48.5\times2=97$. Then subtract 3 from both sides: $x=97 - 3=94$.

Step3: Solve for $y$

We know that $\frac{y + 88}{2}=61$. Multiply both sides by 2: $y + 88=61\times2 = 122$. Then subtract 88 from both sides: $y=122-88 = 34$.

Answer:

$(94,34)$