*The following problems were taken from the*

**GEOMETRY (COMMON CORE)**Regents Exam given on Thursday, January 26, 2017.Previous problems can be found here.

### Part 1

**17. Which rotation about its center will carry a regular decagon onto itself?**

(4) ** 252°**.

A full rotation is 360°. One-tenth of a rotation is 36°, and each one-tenth of a rotation will map a regular decagon onto itself.

Of the choices given, only 252° is a multiple of 36°.

**18. The equation of a circle is x^{2} + y^{2} - 6y + 1 = 0. What are the coordinates of the center and the length of the radius of this circle?
**

(1) *center (0,3) and radius 2(2) ^{1/2}*

First, convert x

^{2}+ y

^{2}- 6y + 1 = 0 to standard form by completing the square.

Half of -6 is -3, and (-3)

^{2}= 9, so add 8 to both sides of the equation to increase 1 to 9.

So x

^{2}+ y

^{2}- 6y + 9 = 8

Then x

^{2}+ (y - 3)

^{2}= 8.

The coordinates of the vertex are (0, 3) and the radius is SQRT(8), which is 2(2)

^{1/2}

Continue to the next problems.

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