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16 Sep 2014, 00:59
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C
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Difficulty:
15%
(low)
Question Stats:
85% (01:58) correct
15%
(02:32)
wrong
based on 75
sessions
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What is the area of the triangle formed by the lines \(2x + 3y = 6\), \(y - x = 2\), and the \(x\)-axis in the coordinate plane?
A. 3
B. 4
C. 5
D. 8
E. 10
A. 3
B. 4
C. 5
D. 8
E. 10
16 Sep 2014, 00:59
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Official Solution:
What is the area of the triangle formed by the lines \(2x + 3y = 6\), \(y - x = 2\), and the \(x\)-axis in the coordinate plane?
A. 3
B. 4
C. 5
D. 8
E. 10
Refer to the diagram below:
The lines \(y = -\frac{2}{3}x + 2\) and \(y = x + 2\) intersect at point \((0, 2)\). This gives us the height of the enclosed triangle, which is 2 units. The \(x\)-intercepts of the lines are as follows: for the line \(y = -\frac{2}{3}x + 2\), it is \((3, 0)\), and for the line \(y = x + 2\), it is \((-2, 0)\). The base of the enclosed triangle is the distance between these two points, which is \(3 - (-2) = 5\) units. The area of the triangle can be calculated as \(\frac{1}{2}* \text{base} *\text{height} = \frac{1}{2}*5 *2 = 5\) square units.
Answer: C
What is the area of the triangle formed by the lines \(2x + 3y = 6\), \(y - x = 2\), and the \(x\)-axis in the coordinate plane?
A. 3
B. 4
C. 5
D. 8
E. 10
Refer to the diagram below:
The lines \(y = -\frac{2}{3}x + 2\) and \(y = x + 2\) intersect at point \((0, 2)\). This gives us the height of the enclosed triangle, which is 2 units. The \(x\)-intercepts of the lines are as follows: for the line \(y = -\frac{2}{3}x + 2\), it is \((3, 0)\), and for the line \(y = x + 2\), it is \((-2, 0)\). The base of the enclosed triangle is the distance between these two points, which is \(3 - (-2) = 5\) units. The area of the triangle can be calculated as \(\frac{1}{2}* \text{base} *\text{height} = \frac{1}{2}*5 *2 = 5\) square units.
Answer: C
27 Aug 2016, 05:09
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I think this is a high-quality question and I agree with explanation.
