SOLUTION: Find the area of a parallelogram bounded by the y-axis, the line x = 2, the line f(x) = 2 + 2x, and the line parallel to f(x) passing through (4, 9). *I have struggling to

Question 1127088: Find the area of a parallelogram bounded by the y-axis, the line
x = 2, the line f(x) = 2 + 2x, and the line parallel to f(x) passing through
(4, 9).
*I have struggling to figure the solution but keep running into confusion. Here is my work so far, so you can see where I am going wrong*
9=2(4)+2
9=8+b
1=b
2x+1=b
Distance formula:(2-4)^2+ (1-9)^2
4 +64
68
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Graph the four lines

to get this parallelogram

I'm going to add in a dashed purple which is 2 units long. This represents the height of the parallelogram

It might be easier to see why this is the height if we rotate the parallelogram so that the shorter side is horizontal to the ground

base = 1 (blue segment)
height = 2 (purple dashed line)

The area of this parallelogram is
Area = base*height = 1*2 = 2

Final Answer: 2 square units

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