Question

find the coordinates of the missing endpoint if b is the midpoint of $overline{ac}$. a(-4,2), b(6,-1)

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 $A(x_1,y_1)=(-4,2)$ and $B(x_m,y_m)=(6,-1)$, and $C(x_2,y_2)$ be the missing endpoint.

Step2: Solve for $x_2$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $6=\frac{-4 + x_2}{2}$. Cross - multiply: $6\times2=-4 + x_2$. Then $12=-4 + x_2$. Add 4 to both sides: $x_2=12 + 4=16$.

Step3: Solve for $y_2$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $-1=\frac{2 + y_2}{2}$. Cross - multiply: $-1\times2=2 + y_2$. Then $-2=2 + y_2$. Subtract 2 from both sides: $y_2=-2 - 2=-4$.

Answer:

$(16,-4)$