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Common Core For Geometry
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 {(x,y) l 1 < x < 10 & 2 < y < 15} , the triangle with vertices at (0,0), (1,3), and (2,1) is {(x,y) l x/2 < y < 3x & y < -2x + 5}.
Finding Systems of Inequalities That Describe Triangular and Rectangular Regions
Classwork
Opening Exercise
Graph each system of inequalities.
a. {𝑦 ≥ 1
𝑥 ≤ 5
i. Is (1,2) a solution? Explain.
ii. Is (1,1) a solution? Explain.
iii. The region is the intersection of how many half-planes? Explain how you know.
b. {𝑦 < 2𝑥 +1
𝑦 ≥ −3𝑥 −2
i. Is (−2,4) in the solution set?
ii. Is (1,3) in the solution set?
iii. The region is the intersection of how many half-planes? Explain how you know.
Exercises 1–3
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