Answer to Question #156524 in Analytic Geometry for yonathan

Question

The vertices of a triangle are F (-3, 6), G (1, -6) and H (5, 2). For line segment FG, there is a midpoint P and Q is the midpoint of FH. a) Show that PQ is parallel to GH b) PQ is half the length of GH

Answer 1

The midpoint theorem states that “The line segment in a triangle joining the midpoints of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

There is given P is the midpoint of FG side and Q is the midpoint of FH side. So, PQ would be midline for $S_{FGH}$ which is parallel to the GH side and $PQ=\frac{GH}{2}.$