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. -------------

Hi, is there a pictorial representation of the triangle that is formed from the above equation?

Based on the information in the stem, to me, the figure that is formed is a square and not a triangle. Since x = -4 forms a straight line parallel to the x-axis and y = x, which translates to y = -4 forms a straight line parallel to the y axis. They both meet at the coordinate (-4.-4), but again, using the x-axis, x = -4 and y = -4 the shape is that of a square not a triangle. Am I missing something?

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.

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