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The area of the region satisfying x ≤ 2, y ≤ IxI and x ≥ 0 is
- a)4 sq. units
- b)1 sq. units
- c)2 sq. units
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The area of the region satisfying x ≤ 2, y ≤IxIand x≥ 0isa)4 ...
Given Information:
The region satisfying the conditions x ≤ 2, y ≤ |x|, and x ≥ 0 needs to be determined.
Solution:
1. Graphical Representation:
To visualize the given conditions, plot the inequalities on a coordinate plane. The region enclosed by these inequalities will be the area of interest.
2. Understanding the Inequalities:
- The inequality x ≤ 2 represents all points to the left of a vertical line passing through x = 2.
- The inequality y ≤ |x| represents all points below or on the curve y = |x|, which is a V-shaped curve symmetric around the y-axis.
- The inequality x ≥ 0 represents all points to the right of the y-axis.
3. Determining the Common Region:
- The common region satisfying all three conditions is the triangle enclosed by the lines x = 0, x = 2, and the curve y = |x|.
- This triangle has a base of length 2 units (from x = 0 to x = 2) and a height of 2 units (corresponding to y = 2 when x = 2).
- Therefore, the area of this triangle is (1/2) * base * height = (1/2) * 2 * 2 = 2 sq. units.
Therefore, the correct answer is option C) 2 sq. units.
The region satisfying the conditions x ≤ 2, y ≤ |x|, and x ≥ 0 needs to be determined.
Solution:
1. Graphical Representation:
To visualize the given conditions, plot the inequalities on a coordinate plane. The region enclosed by these inequalities will be the area of interest.
2. Understanding the Inequalities:
- The inequality x ≤ 2 represents all points to the left of a vertical line passing through x = 2.
- The inequality y ≤ |x| represents all points below or on the curve y = |x|, which is a V-shaped curve symmetric around the y-axis.
- The inequality x ≥ 0 represents all points to the right of the y-axis.
3. Determining the Common Region:
- The common region satisfying all three conditions is the triangle enclosed by the lines x = 0, x = 2, and the curve y = |x|.
- This triangle has a base of length 2 units (from x = 0 to x = 2) and a height of 2 units (corresponding to y = 2 when x = 2).
- Therefore, the area of this triangle is (1/2) * base * height = (1/2) * 2 * 2 = 2 sq. units.
Therefore, the correct answer is option C) 2 sq. units.
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The area of the region satisfying x ≤ 2, y ≤IxIand x≥ 0isa)4 sq. unitsb)1 sq. unitsc)2 sq. unitsd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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