The following points are the vertices of a rectangle. (−3, 3), (4, −2), (−3, −2), (4, 3)
a. Write a system of linear inequalities that
represents the points inside the rectangle.
b. Find the area of the rectangle.

Lesson 2: Finding Systems of Inequalities That Describe

Triangular and Rectangular Regions

Student Outcomes

 Students describe rectangles (with edges parallel to the axes) and triangles in the coordinate plane by means

of inequalities. For example, the rectangle in the coordinate plane with lower left vertex (1,2) and upper right

vertex (10,15) is {(, )│1 ≤ ≤ 10 & 2 ≤ ≤ 15}; the triangle with vertices at (0,0), (1,3), and (2,1) is

bound by ≤ 3, ≥

1

2

, and ≤ −2 + 5.

Lesson Notes

In Algebra I, students graphed the solutions of linear inequalities in two variables as halfplanes and the solution sets of a system of linear inequalities as the intersection of

corresponding half-planes (A-REI.D.12). In this lesson, students are given the region in the

plane and write systems to describe the regions, reversing the process studied in Algebra I.

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step-by-step explanation: