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What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-  [#permalink]

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11 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:18) correct 34% (02:15) wrong based on 289 sessions

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What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8
b) 10
c) 12
d) 14
e) 18

Originally posted by PawanRamnani1234 on 08 Sep 2016, 06:54.
Last edited by Bunuel on 08 Sep 2016, 07:05, edited 1 time in total.
Renamed the topic and edited the question.
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Re: area inscribed by the lines.  [#permalink]

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Check the attached image

We are supposed to find the area of the figure enclosed by the lines x=1, y=1 and y=6-x which is nothing but Area of Triangle ABC.
AB = 4 (distance between (1,1) and (5,1))
AC = 4 (distance between (1,1) and (1,5))

Area of Triangle ABC which is right angled at A = (1/2) * AB * AC = (1/2)*4*4 = 8

Hope it helps!

PawanRamnani1234 wrote:
What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8
b) 10
c) 12
d) 14
e) 18

Looking for appropriate solution for above problem.

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File comment: Figure image.jpg [ 61.4 KiB | Viewed 3718 times ]

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Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-  [#permalink]

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PawanRamnani1234 wrote:
What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8
b) 10
c) 12
d) 14
e) 18

First, let's graph the lines y = 1 and x = 1 At this point, we need to find the points where the line y = 6-x INTERSECTS the other two lines.

For the vertical line, we know that x = 1, so we'll PLUG x = 1 into the equation y = 6-x to get y = 6-1 = 5
Perfect, when x = 1, y = 5, so one point of intersection is (1,5)

For the horizontal line, we know that y = 1, so we'll PLUG y = 1 into the equation y = 6-x to get 1 = 6-x. Solve to get: x = 5
So, when y = 1, x = 5, so one point of intersection is (5,1)

Now add these points to our graph and sketch the line y = 5-x At this point, we can see that we have the following triangle. The base has length 4 and the height is 4
Area = (1/2)(base)(height)
= (1/2)(4)(4)
= 8

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Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-  [#permalink]

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PawanRamnani1234 wrote:
What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8
b) 10
c) 12
d) 14
e) 18

Hi,

The sketches have been made above, but few points..
1) Three equation,so three lines and therefore a triangle..two sides x=1and y=1 make a right angle so we are talking of a RIGHT angle triangle..
2) the third line will intersect these two lines ..
On line x=1, when x is 1 in y=6-x, y=6-1=5.. similarly on line y=1at x=5..
3) therefore the length of each side is 5-1=4..
Area =1/2*4*4=8..
A
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Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-  [#permalink]

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PawanRamnani1234 wrote:
What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8
b) 10
c) 12
d) 14
e) 18

There's no need to actually diagram this problem- simply not much time on the GMAT; however, it might be ok in the beginning. Anyways, the concept behind this question is simply testing your ability to plug in the given y and x values in order to find the two other vertices of the figure- which if you do diagram you'll see is an isosceles equilateral triangle.

1= 6-x
-5=-x
5=x (we're not done yet though)

y=6-(x)
y=6- 1
y= 5 ( we are done yet either)

x and y intersect at (1,1) so actually each length of this triangle would be 4= 4 spots upwards from (1,1) actually gives us (1,5) - the vertice of the triangle derived from plugging in our x value; And 4 spots to the right of (1,1) gives us (5,1) the vertice of the triangle derived from plugging in the y value. And because this triangle is a right triangle (the intersection of two perfectly straight lines, lines with a slope of 0, is 90 degrees and the lines x and y are also perpendicular) the area can be calculated simply by

base1 x base 2 / 2 = area
(4) x (4)/2 =
16/2= 8

Thus

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Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-  [#permalink]

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PawanRamnani1234 wrote:
What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-coordinate plane?

a) 8
b) 10
c) 12
d) 14
e) 18

Let me ask u guys one question

btw I understood this question but here is a doubt

When we are asked to make a graph from a certain equation then we put x=0 and calculate y THEN put y=0 and calculate x and then we plot it

BUT WHY HERE WE TOOK VALUE OF x=1 from the first equation and placed in 3rd equation????
WHY we did that for y as well?

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Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-  [#permalink]

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_________________ Re: What is the area inscribed by the lines y =1, x = 1, y = 6-x on an xy-   [#permalink] 21 Sep 2018, 22:49
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