Question

Line segment $AB$ has endpoints $A\left(2,-3\right)$ and $B\left(-4,6\right)$. What are the coordinates of the midpoint of $AB$?

Answer 1

Find midpoint of line segment $AB$.

The end points of the line segment $AB$ are $A\left(2,-3\right)$ and $B\left(-4,6\right)$.

The midpoint of a line segment with endpoints $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by $C=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

Substituting $\left(2,-3\right)$ for $\left(x_1,y_1\right)$ and $\left(-4,6\right)$ for $\left(x_2,y_2\right)$ in $C=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

$$\begin{gathered} \Rightarrow C=\left\{\frac{2+\left(-4\right)}{2},\frac{6+\left(-3\right)}{2}\right\} \\ \Rightarrow C=\left(\frac{2-4}{2},\frac{6-3}{2}\right) \\ \Rightarrow C=\left(-\frac{2}{2},\frac{3}{2}\right) \\ \therefore C=\left(-1,\frac{3}{2}\right) \end{gathered}$$

Hence, the midpoint of the line segment $AB$ is $C=\left(-1,\frac{3}{2}\right)$.