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A rectangle in the coordinate plane is shown below.  A line with slope 2 splits this rectangle into two regions with equal area.  What is the y-intercept of this line?

 

The rectangle has coordinates (-1,-1), (-1,1), (1,1), and (1,-1).

 May 13, 2025
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A rectangle in the coordinate plane is shown below.  A line with slope 2 splits this rectangle into two regions with equal area.  What is the y-intercept of this line?  The rectangle has coordinates (-1,-1), (-1,1), (1,1), and (1,-1).    

 

Those coordinates draw a square, centered on the origin.    

 

Any straight line through the origin will bisect the square.   

Conversely, any line that bisects the square will pass through the origin.    

 

Therefore, the y-intercept is  (0, 0)    

.    

 May 13, 2025

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