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# The two lines y=x and x=-4 intersect on the coordinate plane

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Manager
Joined: 06 Jul 2011
Posts: 209
Location: Accra, Ghana
The two lines y=x and x=-4 intersect on the coordinate plane  [#permalink]

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23 Apr 2012, 05:54
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87% (00:55) correct 13% (00:39) wrong based on 151 sessions

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The two lines y=x and x=-4 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x axis?

A.\sqrt{}46/3
B. 4\sqrt{}2
C. 8
D. 8\sqrt{}2
E. 16
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: The two lines y=x and x=-4 intersect on the coordinate plane  [#permalink]

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23 Apr 2012, 06:07
1
dzodzo85 wrote:
The two lines y=x and x=-4 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x axis?

A.\sqrt{}46/3
B. 4\sqrt{}2
C. 8
D. 8\sqrt{}2
E. 16

Look at the diagram below:
Attachment:

Area.png [ 9.69 KiB | Viewed 4510 times ]
Both legs of the right triangle equal to 4, so the area is 1/2*4*4=8.

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Manager
Joined: 06 Jul 2011
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Location: Accra, Ghana
Re: The two lines y=x and x=-4 intersect on the coordinate plane  [#permalink]

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23 Apr 2012, 06:23
Thanks a lot for the explanations. I really appreciate it.
Manager
Joined: 28 Jul 2011
Posts: 208
Re: The two lines y=x and x=-4 intersect on the coordinate plane  [#permalink]

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27 Apr 2012, 06:39
Bunuel wrote:
dzodzo85 wrote:
The two lines y=x and x=-4 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x axis?

A.\sqrt{}46/3
B. 4\sqrt{}2
C. 8
D. 8\sqrt{}2
E. 16

Look at the diagram below:
Attachment:
Area.png
Both legs of the right triangle equal to 4, so the area is 1/2*4*4=8.

for line y=x the slope would be m = 1 and y-intersect b = 0

however,i didnot understand how did u draw the line y=x and how did u find the point of intersect. Can u explain that please?

Regards,
Manager
Joined: 28 Jul 2011
Posts: 208
Re: The two lines y=x and x=-4 intersect on the coordinate plane  [#permalink]

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27 Apr 2012, 06:51
kuttingchai wrote:
Bunuel wrote:
dzodzo85 wrote:
The two lines y=x and x=-4 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x axis?

A.\sqrt{}46/3
B. 4\sqrt{}2
C. 8
D. 8\sqrt{}2
E. 16

Look at the diagram below:
Attachment:
Area.png
Both legs of the right triangle equal to 4, so the area is 1/2*4*4=8.

for line y=x the slope would be m = 1 and y-intersect b = 0

however,i didnot understand how did u draw the line y=x and how did u find the point of intersect. Can u explain that please?

Regards,

i think i got it

line 1 x = -4

line 2 y=x

therefore they intersect at y = x i.e. y=-4 therefore (-4,-4)

Hope thats correct way
Math Expert
Joined: 02 Sep 2009
Posts: 47112
Re: The two lines y=x and x=-4 intersect on the coordinate plane  [#permalink]

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27 Apr 2012, 09:02
2
1
kuttingchai wrote:
Bunuel wrote:
dzodzo85 wrote:
The two lines y=x and x=-4 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x axis?

A.\sqrt{}46/3
B. 4\sqrt{}2
C. 8
D. 8\sqrt{}2
E. 16

Look at the diagram below:
Attachment:
Area.png
Both legs of the right triangle equal to 4, so the area is 1/2*4*4=8.

for line y=x the slope would be m = 1 and y-intersect b = 0

however,i didnot understand how did u draw the line y=x and how did u find the point of intersect. Can u explain that please?

Regards,

1. How to draw line y=x?

This line passes thorough all the points with equal x and y-coordinates. Now, pick two such points, for example (0, 0) and (1, 1), and draw a line through them.

This is one of the common lines for the GMAT so it's better to be familiar with it.

2. How to find intersection point of y=x and x=-4

Now, since x=-4 passes through all the points with x-coordinate equal to -4, then naturally intersection point of this line and any other line will have x-coordinate equal to -4. Next, if x-coordinate of intersection point is -4, then line y=x to pass through it, the point must have y-coordinate equal to -4 too: -4=-4. Therefore the coordinates are (-4, -4).

Hope it's clear.
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Re: The two lines y=x and x=-4 intersect on the coordinate plane  [#permalink]

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29 Apr 2012, 03:46
The two lines y=x and x=-4 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x axis?
Ans:
excellent explanation by Bunuel.
these type of questions are easily solved using Graph or drawing lines on co-ordinate axis.

even if you dont know how to draw a graph.
here is solution.
given
y=x and x =-4 intersect.
so, point of intersection between y=x and x =-4 will be (-4,-4)
we have to find the area covered by lines y=x,x=-4 & y=0 (i.e x-axis)
so,
and point of intersection between x=-4 and y=0 will be (-4,0)

so we have a triangle with following axis.(0,0), (-4,0) & (-4,-4)

here, if you can draw a picture of how this line will look in co-ordinate axis, you will find a right angle triangle whose altitude is 4 and base is 4.
so, area will be =1/2 x 4 x 4 = 8 (ans)

if you don't have any idea about how to draw a line or place some points on co-ordinate axis.
remember some old school day formula,
you can calculate the area of triangle by following formula:
1. first calculate the distance between three points by formula ;
Distance (a,b,c) = Sqrt[(x1-x2)^2+(y1-y2)^2]
here, a=4,b=4,c=4sqrt(2)
2. then
calculate s= (a+b+c)/2
and area of triangle is = Sqrt [(s-a)^2+(s-b)^2+(s-c)^2]
after calculation area of triangle will come as 8.

I hope my explanation will be clear.
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Re: The two lines y=x and x=-4 intersect on the coordinate plane  [#permalink]

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13 Sep 2017, 12:21
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Re: The two lines y=x and x=-4 intersect on the coordinate plane &nbs [#permalink] 13 Sep 2017, 12:21
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# The two lines y=x and x=-4 intersect on the coordinate plane

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