How do I solve this problem using Area Integration?

Question

1. (a) Consider the box whose vertices are (-1, 1), (-1, 0), (1, 0), and (1, 1). Let Lm

be the line with slope m that passes through the point (2, 0). Find the value of meR

which divides the box into two halves, each of equal area.

(b) Repeat the problem above, but replace the box with the triangle whose vertices

are (0, 0), (1, 0), and (0, 1).

Answer 1

Calculus is not needed!

Draw and label a diagram.

Add to the diagram the point (-2, 1)

Draw the line (2, 0) to (-2, 1).

Notice that it is the diagonal of both boxes.

What is the slope of that line?