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Three of the four vertices of a rectangle are (5,11), (16,11), and (16,-2).  A line of the form y = 2x + b splits it in half.  What is b?

 Feb 3, 2022
 #1
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b = 12.

 Feb 3, 2022
 #2
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The remaining coordinate of the rectangle is\((5,-2)\).

 

The rectangle is \(13\) tall and \(11\) across. Because the line has a slope of \(2\), the line will be in the shape for \(6.5\) units.

 

We want these \(6.5\) units to be centered across the \(11\) units of the rectangle. This means that there must be \(2.25\) units on each side.

 

This gives us an equation that crosses the points \((13.75,11)\) and \((7.25,-2)\).

 

This means that the equation is y=2x-16.5, so \(\color{brown}\boxed{b=-16.5}\)

 

Here is the image:

 

 

 Feb 4, 2022
edited by BuilderBoi  Feb 4, 2022

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