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

(C) The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height:
A = (1/2) × bh = (1/2) × (4 × 4) = 8
So the area is 8. The correct answer is C.
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Hi, is there a pictorial representation of the triangle that is formed from the above equation?

Thanks.

Here it is:



Triangle ABC is the right triangle (angle ABC = 90 degrees).
AB = 4
BC = 4

THE PROPER PICTURE for the question is posted above in this topic.

Note, that the line x = -4 is parallel to the y-axis and crosses the x-axis at the point (-4, 0).

The line y = x and the line y = -4 are different lines. These two lines cross at the point (-4, -4), which happens to be the crossing point of the lines y = x and x = -4 as well.

The following picture demonstrates that the lines y = x and y = -4 are different:


THE PROPER PICTURE for the question is posted above in this topic.