Question

bc has a midpoint at m(0, -2). point b is at (3, -7). 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 $B(x_1,y_1)=(3,-7)$ and $C(x_2,y_2)$. The mid - point $M(0,-2)$.

Step2: Solve for the x - coordinate of C

We know that $\frac{x_1 + x_2}{2}=0$. Substitute $x_1 = 3$ into the equation: $\frac{3 + x_2}{2}=0$. Multiply both sides by 2: $3+x_2=0$. Then $x_2=-3$.

Step3: Solve for the y - coordinate of C

We know that $\frac{y_1 + y_2}{2}=-2$. Substitute $y_1=-7$ into the equation: $\frac{-7 + y_2}{2}=-2$. Multiply both sides by 2: $-7 + y_2=-4$. Add 7 to both sides: $y_2 = 3$.

Answer:

$C=(-3,3)$