Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Given

$y=-x+2$ ---- (1)

$y = 2x - 1$ --- (2)

$y = x -2$ ---- (3)

Required

The vertices of the triangle

To do this, we simply equate the equations.

Equate (1) and (2)

$-x + 2 = 2x - 1$

Collect like terms

$-x-2x=-2-1$

$-3x=-3$

Divide by -3

$x =1$

Substitute $x =1$ in (1), to get the y-coordinates

$y=-x+2$

$y=-1+2$

$y=1$

So, the coordinate is: (1,1)

Equate (1) and (3)

$-x + 2 = x - 2$

Collect like terms

$-x -x = -2 - 2$

$-2x = -4$

Divide by -2

$x=2$

Substitute $x=2$ in (1) to get the y coordinate

$y=-x+2$

$y=-2+2$

$y=0$

So, the coordinate is (2,0)

Equate (2) and (3)

$2x - 1 = x - 2$

Collect like terms

$2x-x=1-2$

$x=-1$

Substitute $x=-1$ in (2) to get the y coordinates

$y = x -2$

$y=-1-2$

$y=-3$

So, the coordinate is (-1,-3)