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

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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]
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

"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]
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]
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