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When graphed, the three lines y.** 2. y. 2x-1, and y--2 intersect in such a way that they form a triangle
What are the coordinates of the three vertices of this triangle?
-5
7
2
-1
2 3 4 5 6
-1
2
4
5
6
-7
OA (2.0), (0, 2), and (-1,-3)
OB. (0, 2), (2.0), and (1,-1)
OC (1, 1), (2.0), and (-1,-3)
.D. (1,1),(0, 2), and (-1,-3)
Of (2.0), (1, -1), and (-1,-3)

Respuesta :

MrRoyal

Answer:

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

Step-by-step explanation:

Given

[tex]y=-x+2[/tex] ---- (1)

[tex]y = 2x - 1[/tex] --- (2)

[tex]y = x -2[/tex] ---- (3)

Required

The vertices of the triangle

To do this, we simply equate the equations.

Equate (1) and (2)

[tex]-x + 2 = 2x - 1[/tex]

Collect like terms

[tex]-x-2x=-2-1[/tex]

[tex]-3x=-3[/tex]

Divide by -3

[tex]x =1[/tex]

Substitute [tex]x =1[/tex] in (1), to get the y-coordinates

[tex]y=-x+2[/tex]

[tex]y=-1+2[/tex]

[tex]y=1[/tex]

So, the coordinate is: (1,1)

Equate (1) and (3)

[tex]-x + 2 = x - 2[/tex]

Collect like terms

[tex]-x -x = -2 - 2[/tex]

[tex]-2x = -4[/tex]

Divide by -2

[tex]x=2[/tex]

Substitute [tex]x=2[/tex] in (1) to get the y coordinate

[tex]y=-x+2[/tex]

[tex]y=-2+2[/tex]

[tex]y=0[/tex]

So, the coordinate is (2,0)

Equate (2) and (3)

[tex]2x - 1 = x - 2[/tex]

Collect like terms

[tex]2x-x=1-2[/tex]

[tex]x=-1[/tex]

Substitute [tex]x=-1[/tex] in (2) to get the y coordinates

[tex]y = x -2[/tex]

[tex]y=-1-2[/tex]

[tex]y=-3[/tex]

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