Question

the midpoint of $overline{ab}$ is $m(6,2)$. if the coordinates of $a$ are $(7, - 4)$, what are the coordinates of $b$? answer attempt 1 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: Set up equations for x - coordinate

We know $x_1 = 7$, and $\frac{x_1 + x_2}{2}=6$. Substitute $x_1$ into the equation: $\frac{7 + x_2}{2}=6$. Multiply both sides by 2: $7 + x_2=12$. Then solve for $x_2$: $x_2=12 - 7=5$.

Step3: Set up equations for y - coordinate

We know $y_1=-4$, and $\frac{y_1 + y_2}{2}=2$. Substitute $y_1$ into the equation: $\frac{-4 + y_2}{2}=2$. Multiply both sides by 2: $-4 + y_2 = 4$. Then solve for $y_2$: $y_2=4 + 4=8$.

Answer:

$(5,8)$