Question

cd has a mid - point at m(3, 7). point d is at (2, 10). 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 \(C(x_1,y_1)\) and \(D(x_2,y_2)\) with mid - point \(M(x_m,y_m)\) is \(x_m=\frac{x_1 + x_2}{2}\) and \(y_m=\frac{y_1 + y_2}{2}\). We know \(x_m = 3\), \(y_m=7\), \(x_2 = 2\), and \(y_2 = 10\).

Step2: Solve for \(x_1\)

Using \(x_m=\frac{x_1 + x_2}{2}\), substitute the known values: \(3=\frac{x_1+2}{2}\). Multiply both sides by 2: \(6=x_1 + 2\). Then subtract 2 from both sides: \(x_1=4\).

Step3: Solve for \(y_1\)

Using \(y_m=\frac{y_1 + y_2}{2}\), substitute the known values: \(7=\frac{y_1 + 10}{2}\). Multiply both sides by 2: \(14=y_1+10\). Then subtract 10 from both sides: \(y_1 = 4\).

Answer:

\((4,4)\)