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

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The two lines y=x and x=-4 intersect on the coordinate plane [#permalink] New post 23 Apr 2012, 04:54
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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
[Reveal] Spoiler: OA
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Re: The two lines y=x and x=-4 intersect on the coordinate plane [#permalink] New post 23 Apr 2012, 05:07
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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
Area.png [ 9.69 KiB | Viewed 1544 times ]
Both legs of the right triangle equal to 4, so the area is 1/2*4*4=8.

Answer: C.
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Re: The two lines y=x and x=-4 intersect on the coordinate plane [#permalink] New post 23 Apr 2012, 05:23
Thanks a lot for the explanations. I really appreciate it.
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Re: The two lines y=x and x=-4 intersect on the coordinate plane [#permalink] New post 27 Apr 2012, 05:39
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.

Answer: C.



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,
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Re: The two lines y=x and x=-4 intersect on the coordinate plane [#permalink] New post 27 Apr 2012, 05:51
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.

Answer: C.



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
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Re: The two lines y=x and x=-4 intersect on the coordinate plane [#permalink] New post 27 Apr 2012, 08:02
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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.

Answer: C.



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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: The two lines y=x and x=-4 intersect on the coordinate plane [#permalink] New post 29 Apr 2012, 02:46
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] 29 Apr 2012, 02:46
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