Question

the midpoint of $overline{ab}$ is point p at (-16,6). if point a is at (-10,8), what are the coordinates of point b? (-42,20) (-22,4) (-13,7) (2,-5)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is $P(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $A(-10,8)$ and $P(-16,6)$, we can find $x_2$ and $y_2$.
For the x - coordinate:
$\frac{-10+x_2}{2}=-16$

Step2: Solve for $x_2$

Multiply both sides by 2: $-10 + x_2=-32$. Then add 10 to both sides: $x_2=-32 + 10=-22$.

Step3: Solve for $y_2$ using y - coordinate of mid - point formula

For the y - coordinate, $\frac{8 + y_2}{2}=6$. Multiply both sides by 2: $8 + y_2 = 12$. Subtract 8 from both sides: $y_2=12 - 8 = 4$.

Answer:

B. (-22,4)