Leaping Lizards!

Animated films and cartoons are now usually produced using computer technology, rather than the hand-drawn images of the past. Computer animation requires both artistic talent and mathematical knowledge.

Sometimes animators want to move an image around the computer screen without distorting the size and shape of the image in any way. This is done using geometric transformations such as translations (slides), reflections (flips), and rotations (turns) or perhaps some combination of these. These transformations need to be precisely defined, so there is no doubt about where the final image will end up on the screen.

So where do you think the lizard shown on the grid on the following page will end up using the following transformations?  (The original lizard was created by plotting the following anchor points on the coordinate grid and then letting a computer program draw the lizard. The anchor points are always listed in this order: tip of nose, center of left front foot, belly, center  of left rear foot, point of tail, center of rear right foot, back, center of front right foot.)

Original lizard anchor points:

{(12,12),(15,12), (17,12), (19,10),(19,14),(20,13), (17,15), (14,16)}

Each statement below describes a transformation of the original lizard.

Do the following for each of the statements:

•plot the anchor points for the lizard in its new location

•connect the preimage and image anchor points with line segments, or circular arcs, whichever best illustrates the relationship between them

Lazy Lizard

Translate the original lizard so the point at the tip of its nose is located at (24,20), making the lizard appears to be sunbathing on the rock.

Lunging Lizard

Rotate the lizard 90° about point A(12,7) so it looks like the lizard is diving into the puddle of mud.

Leaping Lizard

Reflect the lizard about given line y = x/2 + 16 so it looks like the lizard is doing a back flip over the cactus.

So,

Who to work with? You will work with your elbow partner, but each one of you will have to turn in the assignment. I WILL ONLY CHECK ONE OF THEM, so make sure that you agree with your partners’ work!

What materials do I need? The GeoGebra file “Leaping Lizards” has been shared with you in your Drive/Math1/Module 6 folder.

What do I need to turn in? You will have to turn in

– Three GeoGebra files titled Lazy Lizard, Lunging Lizard, and Leaping Lizard. Share those 3 files with me. Remember to name the files: Math1_PeriodX_Last Name_Title.

– A presentation titled “Conclusions” for each one of the three transformations. You can use the following sentences frames:

• In _________________ the best way to illustrate the relationship between preimage and image is _______________________, but in _________________________________  the best way is________________________________________.
• In _______________  connecting the points shows _____________________________, which means that __________________ _________________________ is always the same.

I recommend you to take a look at Prezi or Thinglink to create your presentations.

How am I going the be given a grade? Here is the rubric for the activity: