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The area of the region bounded by the curves y = |x - 2|, x = 1, x =

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The area of the region bounded by the curves y = |x - 2|, x = 1, x =  [#permalink]

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New post Updated on: 01 Feb 2019, 04:23
3
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A
B
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D
E

Difficulty:

  55% (hard)

Question Stats:

62% (02:31) correct 38% (02:26) wrong based on 47 sessions

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The area of the region bounded by the curves y = |x - 2|, x = 1, x = 5 and the x-axis is _________ sq. units

A) 1
B) 2
C) 3
D) 4
E) 5

Originally posted by 4d on 28 Jan 2019, 23:38.
Last edited by Bunuel on 01 Feb 2019, 04:23, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The area of the region bounded by the curves y = |x - 2|, x = 1, x =  [#permalink]

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New post 29 Jan 2019, 00:53
When x = 1, y = |x-2| = 1
x = 5, y = 3
Plotting this on graph we get,
Base AB = 4.
Height BC = 2
Area = 1/2*AB*BC = 4

D is the answer.
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Re: The area of the region bounded by the curves y = |x - 2|, x = 1, x =  [#permalink]

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New post 01 Feb 2019, 04:20
1
4d wrote:
The area of the region bounded by the curves \(y = \left | x-2 \right | , x = 1, x = 5\) and the \(x-axis\) is _________ sq. units
A) 1
B) 2
C) 3
D) 4
E) 5


As we can see the 4 lines in the rough image below.

Two triangles are formed by the four lines.

Area of ABC = 1/2 * b * h = 1/2 * AB * BC = 1/2 * 1 * 1 = 1/2
Area of CED = 1/2 * CD * ED = 1/2 * 3 * 3 = 9/2

Total Area = 1/2 + 9/2 = 10/2 = 5

Hence the correct answer is E.
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Re: The area of the region bounded by the curves y = |x - 2|, x = 1, x =  [#permalink]

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New post 23 Sep 2019, 04:17
4d wrote:
The area of the region bounded by the curves y = |x - 2|, x = 1, x = 5 and the x-axis is _________ sq. units

A) 1
B) 2
C) 3
D) 4
E) 5


y=x-2: y=0 x=2, and x=0 y=-2, points (2,0;0,-2)
y=-x+2: y=0 x=2, and x=0 y=2, points (2,0;0,2)
x=1 intersects y=x-2 at y=(1)-2=-1, point (1,-1)
x=1 intersects y=-x+2 at y=-(1)+2=1, point (1,1)
x=5 intersects y=x-2 at y=(5)-2=3, point (5,3)
x=5 intersects y=-x+2 at y=-(5)+2=-3, point (5,-3)

plot these points on the plane and you will get two triangles:
triangle a: 1•1/2=0.5
triangle b: 3•3/2=4.5
total area: 5

Answer (E)
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Re: The area of the region bounded by the curves y = |x - 2|, x = 1, x =   [#permalink] 23 Sep 2019, 04:17
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