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Which of the following points is inside a triangle created by three li

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Which of the following points is inside a triangle created by three li  [#permalink]

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New post 06 Feb 2019, 10:42
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (01:30) correct 21% (02:31) wrong based on 19 sessions

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Which of the following points is inside a triangle created by three lines: y = -2x + 100, x-axis, and y-axis?

A. (-20, 60)

B. (30, 45)

C. (20, 40)

D. (40, -20)

E. (50, 50)
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Re: Which of the following points is inside a triangle created by three li  [#permalink]

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New post 06 Feb 2019, 10:55
dreamerchaser wrote:
Which of the following points is inside a triangle created by three lines: y = -2x + 100, x-axis, and y-axis?

A. (-20, 60)

B. (30, 45)

C. (20, 40)

D. (40, -20)

E. (50, 50)


So the best way to solve this question would be to draw it on the co ordinate plan, said that

You can find the points for y = -2x + 100, as x = 50, y =0 & x =0, y =100

When you join these points with the x and y axis you will get a triangle.(You can mark the points with a 10 pt interval)

A,D and E can be eliminated without second thought.

Only C will be visible inside the triangle
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Re: Which of the following points is inside a triangle created by three li  [#permalink]

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New post 06 Feb 2019, 22:05
Find the intersection between the line and respective co-ordinate axis
The triangle formed has the co-ordinates \((0,0) , (50,0)\) and \((0,100)\)
A and D are not in the first quadrant
\(E (50,50)\) clearly lies outside the triangle

For \(B(30, 45)\) and \(C(20, 40)\)
\(y = -2x + 100\)
When we substitute x=30 in the line , we get y=40 [Hence B is above the line, outside the triangle]
When we substitute x=20 in the line , we get y=60 [Hence C is below the line, inside the triangle]
IMO C
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Which of the following points is inside a triangle created by three li  [#permalink]

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New post 08 Feb 2019, 04:40
the line (y = -2x + 100) intersect with x-axis at (50,0) , and with y-axis at (0,100)

A and D can be eliminated as they don't lie in the first quadrant
E is eliminated as (50,50) it is above the (50,0) point of x-intercept

by checking B (30,45): if x=30, then y should be <40, but y = 45 in option B, so eliminated
by checking C (20,40): if x=20, then y should be <60, and y= 40 in option C, which is under the line

so C.
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Which of the following points is inside a triangle created by three li   [#permalink] 08 Feb 2019, 04:40
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Which of the following points is inside a triangle created by three li

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