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In the xy-plane, a triangle has vertexes (0,0), (4,0) and

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Intern
Intern
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B
Joined: 18 Jan 2018
Posts: 38
Location: India
Concentration: Finance, Marketing
GPA: 3.98
Re: In the xy-plane, a triangle has vertexes (0,0), (4,0) and  [#permalink]

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New post 16 Feb 2019, 01:26
Quote:
In the xy- plane, a triangle has vertexes (0,0), (4,0) and (4,5). If a point (x,y) is selected at random from the triangular region, What is the probability that x-y>0 ?

A. 1/5
B. 1/3
c. 1/2
D. 2/3
E. 4/5

Image

We have right triangle with the area = 4*5/2 = 10. Consider the line y<x. All the points which satisfy this equation (are below the line y = x) and lie in the triangular region obviously will have x more than y, which is exactly what we want (as x > y --> x - y > 0).

The probability that the point will be from this region is: (Area of this region)/(Area of the triangle).

Favorable region is also right triangle with vertexes at (0,0) (0,4) and (4,4). As y = x intersects the side of our original triangle at the point (4,4). You''ll see it easily if you draw it. So favorable area = 4*4/2 = 8.

P=810=45P=810=45.

Answer: E.


Bunuel I agree with your answer but is there any way to answer such questions without drawing the diagram altogether or without drawing a diagram as precise as the photo of the graph paper you have shared with your answer?
Director
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Joined: 09 Mar 2018
Posts: 994
Location: India
Re: In the xy-plane, a triangle has vertexes (0,0), (4,0) and  [#permalink]

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New post 16 Feb 2019, 01:47
apoorvasrivastva wrote:
In the xy-plane, a triangle has vertexes (0,0), (4,0) and (4,5). If a point (x,y) is selected at random from the triangular region, What is the probability that x-y>0 ?

A. 1/5
B. 1/3
C. 1/2
D. 2/3
E. 4/5


Visualization is the key here, if we are able to plot these points on the coordinate geometry, then we can actually solve this question very easily

Said that => Total area = 1/2*5*4 = 10

Now x=y will divide the triangle in an area, which will cover most of this triangle,said that

since we need to find x>y, we will consider the area pertaining to the right side of the line x=y which we will initial plot

That area will be ~ 8

Now Probability = 8/10 = 4/5

E
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Re: In the xy-plane, a triangle has vertexes (0,0), (4,0) and   [#permalink] 16 Feb 2019, 01:47

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