







Reflection in the line y = x 
20100721 

From tousif: Find the 2 x 2 matrix which represents a reflection in the line y = x?
Please help.... Answered by Penny Nom. 





An altitude of the triangle intersect a side of the triangle 
20100123 

From Sarah: In what type of triangle does an altitude of the triangle intersect a side of
the triangle at its midpoint??
Sarah Answered by Walter Whiteley. 





Symmetries of a polyhedron 
20090302 

From Vincent: I want to ask is there a formula to find out the number of axes of rotation & plane
of reflection of a 3D figure, like pentagon, pyramid? Answered by Chris Fisher. 





A reflected line segment 
20080714 

From Peter: Segment AB has endpoints A(1,2) and (3,1). Segment AB is reflected over the yaxis such that A becomes A' and B becomes B'. What is the positive difference between the lengths of segment AA' and segment BB'? Answered by Janice Cotcher. 





Two mirrors 
20071024 

From Peter: The reflecting surfaces of two intersecting flat mirrors are at an angle θ (0° < θ < 90°). For a light ray that strikes the horizontal mirror, show that the emerging ray will intersect the incident ray at an angle β = 180° – 2θ. Answered by Stephen La Rocque. 





Mini Golf 
20060817 

From Sarah: I am a sixth grade teacher in Minnesota. I want to have my students explore mini golf and calculate the reflections and angles so that they can figure out how to hit a hole in one. I know that my daughter had various problems like this in eighth grade geometry, but I can't seem to find any internet activities of the appropriate level. Answered by Stephen La Rocque. 





Mini Golf geometry 
20060718 

From Sarah: I want to have my students explore mini golf and calculate the reflections and angles so that they can figure out how to hit a hole in one. I know that my daughter had various problems like this in eighth grade geometry, but I can't seem to find any internet activities of the appropriate level.
If you can steer me towards any resources, I'd be most grateful. Answered by Natasha Glydon. 





A sequence of transformations 
20050103 

From Abraham: Please go to this web site and look at number 31.
http://www.nysedregents.org/testing/mathre/matharch/mathbtestau02.pdf
That is the New York state education web site.
Can you tell me if my answer would be marked correct? My answer was Transformation of 4,3 (T 4,3) followed by a reflection in the xaxis.If I graphed the question and wrote that, would I get full credit Answered by Harley Weston. 





Transformations of pattern blocks 
20030206 

From Cheryl: I am trying to help my 8th grade son with Transformations  use of patttern blocks. He has to trace a figure and reflect it across the xaxis, which I can do, but then it indicates include ordered pairs  that confuses me. Answered by Penny Nom. 





Moving a triangle 
20020418 

From A student: find the verticles of a triangle after it is translated 2 units to the left and then is reflected across the graph of y=x+2. The original verticles of the triangle are (2,0), (3,2), and (6,2). Answered by Peny Nom. 





Reflection off a sphere 
20000512 

From Mark Adami: Given two points P,E and a sphere. Find a point on the sphere, T, so that a line from P that bounces off the sphere at T goes through point E. Answered by Chris Fisher and Harley Weston. 





The three jugs problem 
19990902 

From Kent Lane: I wonder if you could help me figure out this secondary Discrete Math Problem. I cannot figure out where this comes from. Here's the question: You have three containers. Container 1 is a three (3) liter container. Container 2 is a five (5) liter container. Container 3 is an eight (8) liter container that is full of liquid. The goal is to get 4 liters in one of the containers. Stipulations: There are no marks on the containers to measure out the liquid. All you know is that 1 is 3 l., 2 is 5 l., and 3 is 8 l. full of liquid. Answered by Chris Fisher. 





Shapepreserving transformations 
19990504 

From J McAndrew: A shape preserves its shape if a rotation, translation or scaling is performed on it. Are these the only continuous transformations which have this property? These transformations if performed on the parts and then summed have the same effect as the transformation being applied to the whole; are these linear transformations? Who, and what area of mathematics has classified all transformations of this type completely? Answered by Chris Fisher. 





Frieze Patterns 
19980819 

From Brian Bairstow: I am doing a research project on frieze patterns (also called band patterns or border patterns). I know that there are exactly seven different types of frieze patterns, but I have been unable to find a proof for this. If you could tell me this proof, or tell me some internet sites on which I can find material on this, I would be very grateful. Answered by Chris Fisher. 

