What is the y intercept line that is parallel to y=3x, and which bisects the area of rectangle with corners at (0,0),(4,0),(4,2)and(0,2)?

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−7

−6

−5

−4

answer is C.

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Detailed Solution

Midpoint of rectangle =(

\frac{0 + 4}{2}

\frac{0 + 2}{2}

)=(2,1)
Using the given coordinates of the rectangle in the distance formula.
Now we have the linear equation y=3x,
Then the slope of the above line will be

m_{1}

=3
Therefore, the slope of a line parallel to the given line will be

m_{2}

=3
Now the equation of the line with slope 3 and passing through the point (2,1) is
⇒ y−

y_{1}

=m(x−

x_{1}^{}

)
After inserting all the values into the above equation, we get
⇒y−1=3(x−2)
By transferring one side and rearranging the obtained equation in the equation of lin, we get
⇒⇒ y=3x−5
By comparing the obtained equation with the general equation, we get
⇒⇒ y = mx + c
Intersection c = − 5
So option 3 is correct.

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