Friday, 11/12: Double Mirrors
In these questions, the transformation of reflection in a line m is denoted by Rm, reflection in n is denoted by Rn, etc.
Problem 1. Draw a line m so that the reflection Rm maps the shape on the left to the shape on the right. Write the equation of this line. ________________
Problem 2. Draw a line a and a line b so that the composition of reflections RbRa maps the shape on the left to the shape on the right. Write the equations of these lines. Equation for a: ________________ Equation for b: ________________
Problem 3. Suppose line m has equation x = 2. Draw line m and a line n so that the composition of reflections RnRm maps the shape on the left to the shape on the right. Write the equation of line n. Equation for n: ________________
What is the image of the shape on the right by the transformation F = RnRm? _____
What is the image of this shape by G = RmRn? __________
Problem 4. Suppose line p has equation x = 15. Draw line p and a line q so that the composition of reflections RqRp maps the shape on the left to the shape on the right. Write the equation of line q. Equation for q: ________________
Also, draw and describe the image of the shape on the left
by the transformation
T = Rm Rn RqRp. _______________. What is a special name for T?
What is the image of the object on the left by the transformation H = RnRqRp.?______
Identify the transformation H by another name. ___________
Problem 5. Suppose line p has equation x = 15. Draw line p and a line r so that the composition of reflections RpRr maps the shape on the left to the shape on the right. Write the equation of line r. Equation for r: ________________
Problem 6. Write the equations of two lines u and v so that RvRu maps the shape on the left to the shape on the right.
Problem 7. Write the equations a line h so that Rh maps the shape on the left to the shape on the right.
Problem 8. Write the equations of two lines j and k so that RjRk maps the shape on the left to the shape on the right.
