February 11, 2019

On some graph paper, graph the following segments:

y = x, for 0 ≤ x ≤ 2
y = 2x − 2, for 2 ≤ x ≤ 3
x = 3, for 4 ≤ y ≤ 6
y = −x + 9, for 2 ≤ x ≤ 3
y = 7, for 1 ≤ x ≤ 2
y = x + 6, for 0 ≤ x ≤ 1

Now reflect each of the segments over the y-axis.  What popular shape have you drawn?

 

What is the area of the region you have enclosed with this Valentine shape?   

 

If you were to perform a dilation of the complete enclosed region about the point (0, 4) with a scale factor of 2, what would be the area of this new shape?

 

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