Area of a Triangle

Question

Find the area of a triangle bounded by the x-axis, the line f(x)=7−9/5x, and the line perpendicular to f(x) passing through the origin.

Answer 1

The line perpendicular to f(x) has slope  5/9 .  Since it passes through the origin its equation is

 y = (5/9) x. 

This line f(x) intersects the x axis at x = 35/9  Thus the base of the triangle is  35/9.

The height can be obtained by finding the intersection of f(x) and y = (5/9) x as an (x,y) pair.  

Using the method of substitution,  I got ( 315/106 , 175/106)

 

The area of the triangle is then  (1/2) (35/9) ( 175/106) ~ 3.210