Dividing a Triangle

Problem

P is a point on the side AB of a triangle ABC. Find the point Q on BC such that PQ divides the triangle into two equal areas.

Solution 1

M is the midpoint of BC. The area of the triangle ABM is half of the area ABC. Find Q on BC so that ABM=PBQ.

Drag the red point.

Solution 2

Find the point R on the line BC so that ABC=PBR. Q is the midpoint of BR.

Drag the red point.