Question

if the midpoint of a and b(0, 12) is (-5, -1), what are the coordinates of a?
(-5, 11)
(-10, -14)
(-5, -11)
(10, 14)

Explanation:

Step1: Recall mid - point formula

The mid - point formula between 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 the coordinates of point $A$ be $(x,y)$ and point $B=(0,12)$, and the mid - point $M=(-5,-1)$.

Step2: Solve for x - coordinate

We know that $\frac{x + 0}{2}=-5$. Cross - multiply to get $x+0=-10$, so $x = - 10$.

Step3: Solve for y - coordinate

We know that $\frac{y + 12}{2}=-1$. Cross - multiply: $y + 12=-2$. Then subtract 12 from both sides: $y=-2 - 12=-14$.

Answer:

B. (-10, -14)