Q. 99 - Precalculus Enhanced with Graphing Utilities

Question

The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side (see the figure). Find the lengths of the medians of the triangle with vertices at A = (0, 0), B = (6, 0), and C = (4, 4).

Step-by-Step Solution

Answer

The length of the medians are $\sqrt{17},\sqrt{29},2\sqrt{5}$ respectively.

Step 1. Given Information

The coordinate of vertices of triangles are $\left(0,0\right),\left(6,0\right) and \left(4,4\right)$

Step 2. Finding Midpoint

Let the midpoints of AB, BC and CA are $D,E and F$ respectively.

Midpoint of AB, $D=\left(\frac{0+6}{2},\frac{0+0}{2}\right)=\left(3,0\right)$

Midpoint of BC, $E=\left(\frac{6+4}{2},\frac{0+4}{2}\right)=\left(5,2\right)$

Midpoint of CA, $F=\left(\frac{0+4}{2},\frac{0+4}{2}\right)=\left(2,2\right)$