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

Question

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.  4\sqrt{3}

B.  4\sqrt{2}

C. 8

D.  8\sqrt{2}

E. 16

Bunuel · Accepted Answer

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.

Bunuel · Answer

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

dzodzo85 · Answer

Thanks a lot for the explanations. I really appreciate it.

kuttingchai · Answer

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,

kuttingchai · Answer

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

321kumarsushant · Answer

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 
here, a=4,b=4,c=4sqrt(2)
2. then
calculate s= (a+b+c)/2
and area of triangle is = Sqrt  
after calculation area of triangle will come as 8.

I hope my explanation will be clear.

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

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