Question

A triangle is bounded by the x-and y-axes and must pass through P(2,2)

a.) find the area of the triangle as a function of x (Hint: let C be the point (0,2) and D be the point (2,0). Use the fact that ACP and PDB are similar triangles.)

b.) What is the domain of the function you found in a.?

Answer 1

You don't specify what x represents. If we let x be the width of the base of the triangle, then

The domain is all x > 2, since otherwise the line through (2,2) and (x,0) will not bound a triangle in the first quadrant.

The y-intercept of the bounding line can be found using similar triangles:

y/x = 2/(x-2)
y = 2x/(x-2)

So, the area is 1/2 * xy = 1/2 * x*2x/(x-2) = x^2/(x-2)