Question 1183029: Find the area of a parallelogram bounded by the y-axis, the line
x = 4,
the line
f(x) = 4 + 2x,
and the line parallel to f(x) passing through
(2, 6).
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52900)   (Show Source):
You can put this solution on YOUR website! .
Find the area of a parallelogram bounded by the y-axis, the line
x = 4,
the line
f(x) = 4 + 2x,
and the line parallel to f(x) passing through
(2, 6).
~~~~~~~~~~~~~~~~~~~
The line f(x) = 4 + 2x has y-intercept of f(0) = 4 + 2*0 = 4.
The line parallel to f(x) = 4 + 2x and passing through (2,6) is y = Const + 2x
with Const = 6 - 2*2 = 2; so, the parallel line is y = 2 + 2x, and it has y-intercept of y = 2.
Thus, our parallelogram has the base length of 4-2 = 2 units (along the y-axis) and the height of 4 units
(the distance from y-axis to vertical line x= 4).
THEREFORE, the area of our parallelogram is the product of the base and height measures, i.e. 2*4 = 8 square units. ANSWER
Solved.
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! Find the area of a parallelogram bounded by the y-axis, the line
 ,
the line
and the line parallel to  passing through ( ,  ).
The line parallel to  will be of the form
As it passes through (, ), we have
and hence two parallel lines have equations
and
.
As the difference in y-intercepts is ,the side of parallelogram along y-axis is
.
Further, two other parallel lines are  and  and hence vertical distance between them is 
the vertices of the parallelogram are:
A( ,), B(,),
C(, ), and D(, )
The edges AB and CD can be considered the bases; then the length of the bases is and the height is  (the horizontal distance between AB and CD).
The area of a parallelogram is base times height:
 units
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