Geometry Problems of the Day

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 x² + y² - 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 x² + y² - 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 x² + y² - 6y + 9 = 8
Then x² + (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.