Having trouble with coordinates of a line...

[pmcch]

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. √(46)/3
B. 4√2
C. 8
D. 8√2
E. 16

Correct answer: C
Can anyone explain to me why is y= x not the the same as y=-4? And why the lines intersect at the point (-4, -4) ?

[Brent@GMATPrepNow]

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. √(46)/3
B. 4√2
C. 8
D. 8√2
E. 16

To find the point of intersection of the lines y = x and x = -4, solve this "system" of equations.
If x = -4, we'll take the equation, y=x and replace x with -4 to get y = -4
In other words, the point of intersection is at (-4, -4)

Please refer to the image below for the rest of the solution:




Cheers,
Brent

[srcc25anu]

y=x is a 45 degree line from bottom left to top right passing through origin (0,0) and
y=-4 is a horizontal line (// to x-axis) that intersects the x-axis at (0,-4).
On the line y=x, all points have same x and y co-ordinates, so the points on this line will be (1,1) ,(2,2), (3,3) etc. Now if x = -4, y co-ordinate for this point will be -4 also as x=y. so the co-ordinate of intersection (for x=y and for x=-4) will be x = y = -4 hence the point (-4, -4)
Now we need to find area of a triangle with height 4 and base 4 that will be 1/2 * 4 * 4 or 8
hence C is the correct answer.

[pmcch]

Oh! Since x=y all points have the same c and y co-ordinates....
Thank you!!!
Thanks Brent for the visual.