Monday, April 17, 2017

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.

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