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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, 11:42
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A
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C
D
E

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Question Stats:

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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, 11:55
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, 23:05
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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, 05:40
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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Re: Which of the following points is inside a triangle created by three li  [#permalink]

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New post 10 Jun 2019, 18:55
Can someone be so kind and graph the slope y = -2x + 100?

Kind regards!
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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 10 Jun 2019, 22:32
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)



The three points of the triangle are (0,0) (50,0) and (0,100). Clearly, Point A and D have negative x coordinate and are out of contention. Point A and E can be eliminated by substituting x coordinate and checking whether "derived y coordinate" is less than or equal to "given y coordinate". For example, to check option, when we substitute x=50 we should get y equal to 0 but the given value of y is 50 hence E is out as 50 ("given y coordinate") > 0 ("derived y coordinate"). Similarly, Option B can also be eliminated by following this method.

Option C is the correct answer.
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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 11 Jun 2019, 03:20
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jfranciscocuencag wrote:
Can someone be so kind and graph the slope y = -2x + 100?

Kind regards!


here the the three lines:
\(y = -2x+100\) ----> red line
x = 0 ---------> blue line
y = 0 ---------> green line

(you can use: https://www.desmos.com/calculator)
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Screenshot_2019-06-11 Desmos graph.png
Screenshot_2019-06-11 Desmos graph.png [ 15.89 KiB | Viewed 279 times ]


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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 11 Jun 2019, 15:48
Mahmoudfawzy83 wrote:
jfranciscocuencag wrote:
Can someone be so kind and graph the slope y = -2x + 100?

Kind regards!


here the the three lines:
\(y = -2x+100\) ----> red line
x = 0 ---------> blue line
y = 0 ---------> green line

(you can use: https://www.desmos.com/calculator)


Mahmoudfawzy83 Thank you!

Just one question, how do we know that the line is going to be drown in that quadrant?
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Which of the following points is inside a triangle created by three li  [#permalink]

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New post 11 Jun 2019, 16:09
[quote="jfranciscocuencag" how do we know that the line is going to be drown in that quadrant?[/quote]

we are talking about infinite straight lines, so:
In general, most line pass through 3 quadrants (in our case, our line pass through Q1,Q2,Q4) ... but lines passing through the origin, cut through 2 quadrants only.

after rearranging the equation so that "y" (with positive sign) is in one side and anything else is in the other side, see the sign of "x",
if it is (+ve), so it pass through Q1 and Q3 for sure.
if it is (-ve), so it pass through Q2 and Q4 for sure. (like in our question)

In our question, the line is making a triangle with x-axis and y axis.
the triangle has 3 points:
(0,0), (x,0) and (0,y)

to know (x,0) ---> let y = 0 in the equation , and x will be 50, making (50,0)
to know (0,y) ---> let x = 0 in the equation , and y will be 100, making (0,100)

draw it roughly, and you will find that the triangle is in Q1

I hope this suffices your question.
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Which of the following points is inside a triangle created by three li   [#permalink] 11 Jun 2019, 16:09
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