Question

the midpoint of $overline{ab}$ is $m=(3,0)$. one endpoint is $a=(7, - 6)$. find the coordinates of the other endpoint, $b$.

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 $x_1 = 7$, $y_1=-6$, and $M(3,0)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=3$. Substitute $x_1 = 7$ into the equation: $\frac{7 + x_2}{2}=3$. Multiply both sides by 2: $7 + x_2=6$. Then subtract 7 from both sides: $x_2=6 - 7=-1$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=0$. Substitute $y_1=-6$ into the equation: $\frac{-6 + y_2}{2}=0$. Multiply both sides by 2: $-6 + y_2=0$. Then add 6 to both sides: $y_2 = 6$.

Answer:

$B=(-1,6)$