## Saturday, October 02, 2021

### 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 ry = 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.

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