Question

b is the midpoint of line segment $overline{ac}$. the coordinates of b are (-1, 8) and the coordinates of a are (-10, -12). what are the coordinates of c? a (-5.5, -2) b (-2, -5.5) c (28, 8) d (8, 28)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A=(x_1,y_1)=(-10,-12)$, $B = (-1,8)$ and $C=(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-1$. Substitute $x_1=-10$ into the equation: $\frac{-10 + x_2}{2}=-1$. Multiply both sides by 2: $-10+x_2=-2$. Then $x_2=-2 + 10=8$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=8$. Substitute $y_1=-12$ into the equation: $\frac{-12 + y_2}{2}=8$. Multiply both sides by 2: $-12+y_2 = 16$. Then $y_2=16 + 12=28$. So the coordinates of $C$ are $(8,28)$.

Answer:

D. (8, 28)