SOLUTION: Find the area of a parallelogram bounded by the y-axis, the line x = 7, the line f(x) = 5 + 2x, and the line parallel to f(x) passing through (4, 12).

Question 1135855: Find the area of a parallelogram bounded by the y-axis, the line
x = 7, the line f(x) = 5 + 2x, and the line parallel to f(x) passing through
(4, 12).

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The line parallel to y=2x+5 passing through (4,12) has the equation y = 2x+4.

With the sides of the parallelogram defined by x=0, x=7, y=2x+4, and y=2x+5, the vertices of the parallelogram are A(0,4), B(0,5), C(7,19), and D(7,18).

The edges AB and CD can be considered the bases; then the length of the bases is 1 and the height is 7 (the horizontal distance between AB and CD).

The area of a parallelogram is base times height:

ANSWER: The area of the parallelogram is 1*7 = 7.
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