Question

(30 points)

Answer 1

The vertices of the triangle are the points where any pair of lines intersect.

We start by setting up the system

$\begin{cases}y=-x+2\\y=2x-1 \end{cases} \iff -x+2=2x-1 \iff 3x=3 \iff x=1$

Using one of the two equations we can derive the correspondent y value:

$f(x)=-x+2 \implies f(1)=-1+2 = 1$

So, one vertex is (1, 1)

We choose the other two pairs of lines to find the other vertices:

$\begin{cases}y=-x+2\\y=x-2 \end{cases} \iff -x+2=x-2 \iff x=2 \implies y = 0$

$\begin{cases}y=x-2\\y=2x-1 \end{cases} \iff x-2=2x-1 \iff x=-1 \implies y=-3$

So, the three vertices are (1, 1), (2, 0), (-1, -3).