Question

question
the midpoint of $overline{ab}$ is $m(0,2)$. if the coordinates of $a$ are $(1,3)$, what are the coordinates of $b$?

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $A(x_1,y_1)=(1,3)$ and $B(x_2,y_2)$. The mid - point $M(0,2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=0$. Substitute $x_1 = 1$ into the equation: $\frac{1+x_2}{2}=0$. Multiply both sides by 2: $1 + x_2=0$. Then $x_2=-1$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=2$. Substitute $y_1 = 3$ into the equation: $\frac{3 + y_2}{2}=2$. Multiply both sides by 2: $3 + y_2 = 4$. Then $y_2=1$.

Answer:

$(-1,1)$