Question

Triangle MNP has vertices $M\left(3,5\right),N\left(-2,8\right)\text{and}P\left(7,-4\right)$. Find the coordinates of midpoint of each side.

Short answer

The coordinates of midpoint of the line segment are MN, NPand PMrespectively are$\left(\frac{1}{2},\frac{13}{2}\right),\left(2.5,2\right)\text{and}\left(5,0.5\right)$respectively.

Step-by-step solution

Step 1. Write down the given information.

The given line segment with end-points has coordinates $\left(4.3,-2.1\right)\text{and}\left(1.9,7.5\right)$.

Step 2. Concept used.

If a line segment has end-points at $\left(x_1,y_1\right)\text{and}\left(x_2,y_2\right)$ then the midpoint of the segment has coordinates $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

Step 3. Calculation.

The given triangle MNP has vertices $M\left(3,5\right),N\left(-2,8\right)\text{and}P\left(7,-4\right)$.

$\begin{array}{c}\text{Midpointof}MN=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{3-2}{2},\frac{5+8}{2}\right)\\ =\left(\frac{1}{2},\frac{13}{2}\right)\end{array}$$\begin{array}{c}\text{Midpointof}NP=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{-2+7}{2},\frac{8-4}{2}\right)\\ =\left(\frac{5}{2},\frac{4}{2}\right)\\ =\left(2.5,2\right)\end{array}$$\begin{array}{c}\text{Midpointof}PM=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{7+3}{2},\frac{-4+5}{2}\right)\\ =\left(\frac{10}{2},\frac{1}{2}\right)\\ =\left(5,0.5\right)\end{array}$

Step 4. Conclusion.

The coordinates of midpoint of the line segment are MN, NPand PMrespectively are $\left(\frac{1}{2},\frac{13}{2}\right),\left(2.5,2\right)\text{and}\left(5,0.5\right)$respectively.