2. 外语
  3. In the xy-plane, triangular region R is bounded by the lines x = 0, y = 0, and 4x + 3y = 60. Which of the following points lie i

In the xy-plane, triangular region R is bounded by the lines x = 0, y = 0, and 4x + 3y = 60. Which of the following points lie i

admin2017-10-16  29
问题 In the xy-plane, triangular region R is bounded by the lines x = 0, y = 0, and 4x + 3y = 60. Which of the following points lie inside region R ? Indicate all such points.
选项 A、(2,18)
B、(5,12)
C、(10,7)
D、(12,3)
E、(15,2)
答案B，D
解析 Consider the three lines that bound triangular region R. The line x = 0 is the y-axis, and the line y = 0 is the x-axis. The line 4x + 3y = 60 intersects the x-axis at(15, 0)and intersects the y-axis at(0, 20). The figure below shows region R.

From the figure, you can see that all points inside region R have positive coordinates and lie below the line 4x + 3y = 60. Note that the equation 4x + 3y = 60 can be rewritten in the form y =. In this form, you can see that points inside region R satisfy the inequality y <. Since all of the answer choices have positive coordinates, you need only to check whether the coordinates in each answer choice satisfy the inequality y<, or equivalently 4x+ 3y<60.
Choice A,(2, 18): 4x + 3y = 4(2)+ 3(18)= 62>60. So Choice A is not in region R.
Choice B,(5, 12): 4x + 3y = 4(5)+ 3(12)= 56<60. So Choice B is in region R.
Choice C,(10, 7): 4x + 3y = 4(10)+ 3(7)= 61>60. So Choice C is not in region R.
Choice D,(12, 3): 4x + 3y = 4(12)+3(3)= 57 < 60. So Choice D is in region R.
Choice E,(15, 2): 4x + 3y = 4(15)+3(2)= 66 > 60. So Choice E is not in region R.
Thus the correct answer consists of Choices B and D.
This explanation uses the following strategies.
Strategy 3: Translate from an Algebraic to a Graphical Representation
Strategy 8: Search for a Mathematical Relationship
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