Question

the midpoint of ab is m(0, -1). if the coordinates of a are (8, -3), what are the coordinates of b?

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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1 = 8$, $y_1=-3$, and $M(0,-1)$.

Step2: Find the x - coordinate of B

Set up the equation for the x - coordinate of the mid - point: $\frac{x_1 + x_2}{2}=0$. Substitute $x_1 = 8$ into it: $\frac{8 + x_2}{2}=0$. Multiply both sides by 2: $8 + x_2=0$. Then solve for $x_2$: $x_2=-8$.

Step3: Find the y - coordinate of B

Set up the equation for the y - coordinate of the mid - point: $\frac{y_1 + y_2}{2}=-1$. Substitute $y_1=-3$ into it: $\frac{-3 + y_2}{2}=-1$. Multiply both sides by 2: $-3 + y_2=-2$. Then solve for $y_2$: $y_2 = 1$.

Answer:

$(-8,1)$