Questions: Given: The coordinates of triangle PQR are P(0,0), Q(2a, 0), and R(2b, 2c). Prove: The line containing the midpoints of two sides of a triangle is parallel to the third side. As part of the proof, find the midpoint of PR. (b, c) (a-b, c)

Solution Steps

The coordinates of point P are (0, 0). The coordinates of point R are (2b, 2c).

The midpoint formula is given by: Midpoint = $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$

Substituting the coordinates of P and R into the midpoint formula: Midpoint of PR = $\left(\frac{0 + 2b}{2}, \frac{0 + 2c}{2}\right)$

Midpoint of PR = $\left(\frac{2b}{2}, \frac{2c}{2}\right)$ Midpoint of PR = (b, c)

Final Answer