Question

(30 points)

When graphed, the three lines y = -x + 2, y = 2x − 1, and y = x − 2 intersect in such a way that they form a triangle.

What are the coordinates of the three vertices of this triangle?



A.

(2, 0), (0, 2), and (-1, -3)

B.

(0, 2), (2, 0), and (1, -1)

C.

(1, 1), (2, 0), and (-1, -3)

D.

(1, 1), (0, 2), and (-1, -3)

E.

(2, 0), (1, -1), and (-1, -3)

Answer 1

(1, 1), (2, 0), and (-1, -3)

Explanation:

I got right on the test.

Answer 2

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).