Geometry Problems of the Day (Geometry Regents, January 2013)

Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

Geometry Regents, June 2013

Part II: Each correct answer will receive 2 credits. Partial credit is possible.


29. After the transformation r_{y = x}, the image of triangle ABC is triangle A'B'C'. If AB = 2x + 13 and A'B' = 9x - 8, find the value of x.

Answer:

A reflection is a rigid transformation which preserves distance. So the length of AB = the length of A'B'.

9x - 8 = 2x + 13
7x = 21
x = 3

30. In the diagram below, circles A and B are tangent at point C and AB is drawn. Sketch all common tangent lines.

Answer:

There are three common tangents: One connecting the tops, one connecting the bottom, and one through the intersection point of the two circles.

Check out the image below. It's a sketch, so it doesn't have to be perfect, but don't get sloppy.

31. On the set of axes below, graph the locus of points 4 units from (0,1) and the locus of points 3 units from the origin. Label with an X any points that satisfy both conditions.

Answer:

Each locus is going to be a circle about the stated point. The two circles will intersect in at the point (0, -3), where you need to draw an X.

Look at the image below:

More to come. Comments and questions welcome.

More Regents problems.

I also write Fiction! You can now preorder Devilish And Divine, edited by John L. French and Danielle Ackley-McPhail, which contains (among many, many others) three stories by me, Christopher J. Burke about those above us and from down below. Preorder the softcover or ebook at Amazon. Also, check out In A Flash 2020, by Christopher J. Burke for 20 great flash fiction stories, perfectly sized for your train rides. Available in softcover or ebook at Amazon. If you enjoy it, please consider leaving a rating or review on Amazon or on Good Reads.