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.


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.


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.


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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