Question

Find the midpoint of the segment with the given endpoints.

$\left(-3,4\right),\left(4,-2\right)$

Short answer

The midpoint of the segment with the endpoints$\left(-3,4\right),\left(4,-2\right)$ is$\left(\frac{1}{2},1\right)$ .

Step-by-step solution

Step 1. Given Information.

The given endpoints are$\left(-3,4\right),\left(4,-2\right)$ .

Step 2. Formula used.

The midpoint of the segment with the endpoints$\left(x_1,y_1\right),\left(x_2,y_2\right)$is$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

Step 3. Calculation.

To find midpoint of the segment, substitute$\left(x_1,y_1\right)=\left(-3,4\right)$and$\left(x_2,y_2\right)=\left(4,-2\right)$into the midpoint formula then simplify it.

$\begin{array}{l}\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{-3+4}{2},\frac{4-2}{2}\right)\\ \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(\frac{1}{2},1\right)\end{array}$

Step 4. Conclusion.

The midpoint of the segment with the endpoints $\left(-3,4\right),\left(4,-2\right)$is$\left(\frac{1}{2},1\right)$ .