Graph triangles

Use the information about the triangles on this graph to find the coordinates of the point where they touch.

Problem



This is the graph of the line $y=-2x+12$.
Image
Graph Triangles


Point P is on this line.

The ratio of the area of the red triangle to the area of the blue triangle is $1:4$.

Find the coordinates of point $\text P$.

This problem is adapted from the World Mathematics Championships