## MATHCOUNTS Valentine

February 11, 2019

Topics/Content Areas:

On some graph paper, graph the following segments:

*y* = *x*, for 0 ≤ *x* ≤ 2

*y* = 2*x* − 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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