Question

question
the midpoint of $overline{ab}$ is $m(2,0)$. if the coordinates of $a$ are $(-2,3)$, 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 $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(2,0)$, $A(-2,3)$, let the coordinates of $B$ be $(x,y)$.

Step2: Solve for $x$

We have $\frac{-2 + x}{2}=2$. Multiply both sides by 2: $-2 + x = 4$. Then add 2 to both sides: $x=4 + 2=6$.

Step3: Solve for $y$

We have $\frac{3 + y}{2}=0$. Multiply both sides by 2: $3 + y = 0$. Then subtract 3 from both sides: $y=-3$.

Answer:

$(6,-3)$