Find the area of the shaded region

5x^2 +24x +1

Step-by-step explanation:

First you'll want to find the area of the larger rectangle, and then you'll subtract the area of the smaller rectangle (which is not shaded) to get your answer.

Larger Rectangle:

A = length * width

A = (2x + 3)(4x - 5) = (8x^2 - 10x + 12x - 15) = 8x^2 + 2x - 15

Smaller Rectangle:

A = length * width

A = (x - 8)(3x + 2) = (3x^2 + 2x - 24x - 16) = 3x^2 - 22x - 16

Larger Rectangle minus Smaller Rectangle:

(8x^2 + 2x - 15) - (3x^2 - 22x - 16)

5x^2 +24x +1

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.