Question

Find the coordinates of the midpoint of $\overline{AB}$. (You may want to draw an diagram.)

$A(0,1)$, $B(0,5)$

Short answer

The coordinates of the midpoint of$\overline{AB}$ is $(0,3)$.

Step-by-step solution

Step 1. Write the formula to find the coordinates of the midpoint of the line joining the points Ax1,y1and Bx2,y2.

The formula to find the coordinates of the midpoint of the line joining the points $\mathbf{A}\left({\mathbf{x}}_1\mathbf{,}{\mathbf{y}}_1\right)$and$\mathbf{B}\left({\mathbf{x}}_2\mathbf{,}{\mathbf{y}}_2\right)$is $\left(\frac{{\mathbf{x}}_1\mathbf{+}{\mathbf{x}}_2}{2}\mathbf{,}\frac{{\mathbf{y}}_1\mathbf{+}{\mathbf{y}}_2}{2}\right)$.

Step 2. Find the coordinates of the midpoint of the line joining the points A(0, 1) and B(0, 5).

The coordinates of the midpoint of the line joining the points $A(0,1)$and $B(0,5)$is given by:

$\begin{array}{c}\left(\frac{0+0}{2},\frac{1+5}{2}\right)=\left(\frac{0}{2},\frac{6}{2}\right)\\ =\left(0,3\right)\end{array}$

Step 3. Write the conclusion.

The coordinates of the midpoint of the line joining the points $A(0,1)$ and $B(0,5)$ is $(0,3)$.