Lesson 1 Leaping Lizards! Develop Understanding

Jump Start

Given the pre-image point located at as shown in the diagram, find the location of the image point if point is:

  1. Reflected over the -axis.

  2. Reflected over the -axis.

  3. Rotated counterclockwise around the origin.

  4. Rotated clockwise around the origin.

  5. Translated left and up .

a coordinate plane with point A at (5,2) x–4–4–4–2–2–2222444y–4–4–4–2–2–2222444000

Learning Focus

Identify features of translations, rotations, and reflections.

What tools and strategies do I use when I translate a figure? Rotate a figure? Reflect a figure?

What do these tools and strategies reveal about the transformation?

Although each of these transformations move figures in different ways, what do they all have in common?

Open Up the Math: Launch, Explore, Discuss

Animated films and cartoons are now usually produced using computer technology, rather than the hand-drawn images used in 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 the three. These transformations need to be precisely defined, so there is no doubt about where the final image will end up on the screen.

Today you will be animating the lizard shown on your handout by transforming it in various ways. 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:

Each statement below describes a transformation of the original lizard. Do the following for each of the transformations:

  • Plot the anchor points for the lizard in its new location.

  • Connect the pre-image and image anchor points with line segments or circular arcs, whichever best illustrates the relationship between them.

1.

Lazy Lizard

Translate the original lizard so the point at the tip of its nose is located at , making the lizard appear to be sunbathing on the rock.

a coordinate plane with images of a cactus, lizard, rock, sun, and mud puddle 555101010151515202020252525303030555101010151515202020252525303030000

2.

Lunging Lizard

Rotate the lizard about the point so it looks like the lizard is diving into the puddle of mud.

a coordinate plane with images of a cactus, lizard, rock, sun, and mud puddle 555101010151515202020252525303030555101010151515202020252525303030000