Wedged triangles

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In this resource students are given an image of a reciprocal curve, y=k/x. Two tangents to the curve are used, together with the coordinate axes, to form an 'arrow head' quadrilateral under the curve. The challenge is to determine the area of the quadrilateral.

The first step towards solving the problem involves determining the equation of the reciprocal, which is achieved by substitution of either of the given points. Differentiation yields the gradients of the tangents, leading on to finding the equation of the line in each case.

An extension to the problem develops the situation further by reflecting one of the points of intersection and drawing the resulting triangle. Combining the triangles yields an arrow head. The task becomes one of finding the area of the arrowhead.

 

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