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Age 14 to 16 Short Challenge Level:

This is the graph of the line $y=-2x+12$.Diagram showing the graph y=-2x+12. A point P on the line divides the segment in the positive quadrant into two segments. The upper segment determines a blue triangle by drawing the line parallel to the x axis, and the lower segment determines a red triangle by drawing the line parallel to the y axis.

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
You can find more short problems, arranged by curriculum topic, in our short problems collection.