Length of Triangle Medians

**dizzycarly** · June 16th 2009, 02:13 PM

I need help with my homework

The triangle PQR has the following coordinates, P(-2,4) Q(-4,-4) R(6,0)
Calculate the thre medians of the triangle using the midpoint fomula.

Fomula: M = (x1+x2/2), (y1+y2/2)

Can you help me out?

**yeongil** · June 16th 2009, 02:33 PM

You start by using the midpoint formula three times. First, find the midpoint of PQ. Let (x1, y1) be P(-2, 4) and let (x2, y2) be Q(-4, -4):

$\begin{aligned}<br /> M_{PQ} &= \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \\<br /> &= \left(\frac{-2 + (-4)}{2}, \frac{4 + (-4)}{2}\right) \\<br /> &= (-3, 0)<br /> \end{aligned}$

You have two points to find the equation of this median $M_{PQ} (-3, 0)$ and R(6, 0). Find the slope, use point-slope form or slope-intercept form to find this equation. You'll see that the equation is y = 0.

Repeat the process to find the midpoint of QR. Let (x1, y1) be Q(-4, -4) and let (x2, y2) be R(6,0). Find the equation of the line between $M_{QR}$ and P. Then do it one last time for PR, and find the equation of the line between $M_{PR}$ and Q.

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