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Geometry of Equations

Food for thought

Between the lines
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Problem

In the diagram below \(f(x)\) is a linear function.

The area of the green shaded region (above the \(x\)-axis) is \(12\) square units.

A parallelogram formed by lines y = f(x) passing through the origin, y = f(x) minus k and x=2, 8. The region above the x axis is shaded green, the region below is shaded blue.

What is the area of the blue shaded region (below the \(x\)-axis)?