Lines of Symmetry/Rotational Symmetry/Vectors/Algebra Problems
Line symmetry: can the shape/object be folded over a line to make it look exactly the same as the original?
Rotational Symmetry: can the shape/object be rotated around its center a certain amount of degrees to map it onto itself? We exclude 0 and 360 degrees.
Draw the lines of symmetry in the following objects or shapes.
Determine the amount of degrees of rotational symmetry in the following shapes.
Translation Vectors
Translation vectors are another way to think about translations. Instead of the normal notation we are used to, ), we now represent this translation using a vector. A vector has both direction (which way to move an object) and magnitude (how far to move an object). Below we will find three examples see if you can complete the translation using the vector and then write the translation in notation form.
Notation Form:
Notation Form:
Draw the translation vector.
Notation Form:
Composites of Reflections
In Geometry we sometimes like to look at a composite of reflections and see if we can do that sequence of transformations in one move, especially with reflections. Reflecting over a combination of parallel lines or intersecting will yield a special single transformation. Let us see if we can come up with some rules for certain situations.
Situation #1-Reflecting over a pair of parallel lines
Reflect over the line y=4 followed by a reflection over the line y=-3.
a)Write the sequence transformations in composition notation.
b)Is there a single transformation that could yield the same result?
c)Do you see anything you could write a rule about?
a)Write the sequence of transformations in words.
b)Is there a single transformation that could yield the same result?
c)Do you see a relationship between the distance of the parallel lines and the distance of the original image and final image?
Situation #2-Reflecting over intersecting lines
Reflect over the y-axis followed by a reflection over the x-axis.
a)Write the sequence of transformation in composition notation.
b)Is there a single transformation that would yield the same result?
c)Do you see any rules that you could write about?
Things to look at in the problem above: What angle do the two lines you are reflecting over make? What is your single transformation?
Try this one now!
a)reflect over line l followed by a reflection over line m.
b)Could you perform a single transformation that would yield the same result?
c)Rule?