I need to make a trapezoid using systems of inequalities. The coordinates are (-2,3), (2,3), (-3,0), (3,0).

The teacher said there is a way to use two absolute value equations and one plain linear equation. Can someone help me. EASY 10 POINTS!

P.S The inside of the trapezoid need to be the solution or colored in part.

## Answers (1)

For the sides,

the line from 2,3 to 3,0 is

y = (3 - 0) / (2 - 3) * x + b

y = -3 x + b

0 = -9 + b

b = 9

y = -- 3x + 9 (right side)

And the other one is

y = 3x + 9 (left side)

So you can describe the region which is the trapezoid in 3 ranges:

-3 <= x < -2:

. . . . . 0 <= y <= 3x + 9 (triangle on left side)

-2 <= x < 2:

. . . . . 0 <= y <= 3 (rectangle in the middle)

2 <= x < 3:

. . . . . 0 <= y <= -- 3x + 9 (triangle on the right)

Maybe your teacher had in mind to combine the first and third of those into

2 <= | x | <= 3: 0 <= y <= -- 3 |x| + 9 (covers both triangles)

along with the second one

-2 <= x < 2: 0 <= y <= 3 (rectangle in the middle)