8
algebra

A region is defined by x+y6x + y \leq 6, x2x \geq 2, y1y \geq 1. What is the shape of this region?

A

Triangle

B

Square

C

Trapezoid

D

Unbounded

Correct Answer: A

Choice A is the correct answer. Find the vertices.

  1. Intersection 1 (x=2,y=1x=2, y=1): (2,1)(2, 1) (Valid: 2+162+1 \leq 6)
  2. Intersection 2 (x=2,x+y=6x=2, x+y=6): 2+y=6y=42+y=6 \rightarrow y=4. Vertex (2,4)(2, 4).
  3. Intersection 3 (y=1,x+y=6y=1, x+y=6): x+1=6x=5x+1=6 \rightarrow x=5. Vertex (5,1)(5, 1).
  4. Shape: Three vertices (2,1),(2,4),(5,1)(2,1), (2,4), (5,1) form a right triangle.

?�� Strategic Tip: Sketch the lines to visualize the enclosed region.

Choice B is incorrect because it has 3 sides, not 4. Choice C is incorrect because it has 3 sides. Choice D is incorrect because the region is enclosed by the three lines.