Chapter 14.1, Problem 26PSC

To determine

To write an equation for the locus of the points $(x,y)$ such that the area of the triangle with vertices $(x,y),(0,0)$ and $(3,0)$

Answer to Problem 26PSC

  $y=\pm \frac{4}{3}$

Explanation of Solution

Given:

The triangle with vertices $(x,y),(0,0)$ and $(3,0)$ .

Calculation:

The following figure shows the triangle with vertices $(x,y),(0,0)$ and $(3,0)$

  

The area of above triangle is given by

  $\begin{array}{l}{A}_{△}=\frac{1}{2}bh\\ 2=\frac{1}{2}(3)h\\ h=\frac{4}{3}\\ y=\pm h\\ y=\pm \frac{4}{3}\end{array}$

And $x$ is for all real numbers.