A Mathy Valentine

February 12, 2018

On a coordinate grid, 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 enclosed region graphed in the previous problem?

 

If the graph from the first problem is dilated about the point (0, 4) with a scale factor of 2, what is the new area of the enclosed region?

 

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