Question

the midpoint of $overline{ab}$ is $m(-2,-3)$. if the coordinates of $a$ are $(-8,-5)$, what are the coordinates of $b$? answer attempt 2 out of 2

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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Find the x - coordinate of B

We know $M_x=-2$, $x_1=-8$. Using the x - part of the mid - point formula $\frac{x_1 + x_2}{2}=M_x$, we substitute the values: $\frac{-8 + x_2}{2}=-2$. Multiply both sides by 2: $-8 + x_2=-4$. Then add 8 to both sides: $x_2 = 4$.

Step3: Find the y - coordinate of B

We know $M_y=-3$, $y_1=-5$. Using the y - part of the mid - point formula $\frac{y_1 + y_2}{2}=M_y$, we substitute the values: $\frac{-5 + y_2}{2}=-3$. Multiply both sides by 2: $-5 + y_2=-6$. Then add 5 to both sides: $y_2=-1$.

Answer:

$(4, -1)$