Rotating a Triangle 180 degrees clockwise and counterclockwise

What is the difference between rotating a triangle 180 degrees clockwise vs. 180 degress counterclosckwise?

What happens to the coordinates after the rotation?

Welcome to I.S. 223's iteach/ilearn grade 8 math professional development.

Please comment any time before, during, or after the class.

Some sites we will use today are:

The iTeach/ilearn website

Mathsnet interactive transformaitons

Visual discription of a the three types of transformations.

Difficult examples of transformations

Two successive reflections

Good interactive examples of rotation

How do we rotate a figure 90 degrees clockwise?

Edit Preferences ------ change the units from hundredths to ones. Be sure to check off apply to this sketch and to new sketches.

Create a geometric figure using the line segment tool
Probably the easiest to work with is a right triangle.
A (-7.7)
B (-2,1)
C (-7,1)

Be sure that all parts of your figure are deselected. Use the selection tool to click outside of your figure.
Using the selection tool choose each of the point on your figure.
Display ------ Label Points

Transform ----- Mark Center Alternatively, you can double click the origin (0,0. This indicates that you want to rotate the figure - right triangle - about the origin.

Use the selection tool to select the figure - right triangle - for rotation.

Transform ----- Rotate (90 degrees)

Using the selection tool, click outside the rotated figure. With the selection tool. choose only the points on the rotated figure.

Display ----- Show Labels

Reflecting over the Y Axis

Use the line segment tool to connect these point. You will create the points while creating line segments.
(-2, 1)
(-5, 5)
(-7. 2)
and back to (-2, 1).
Click the selection tool outside of the triangle to assure that no points or segments are selected.
Using the selection tool click each point on the triangle separately.
Display ----- Label Points
Mark the Y Axis for the reflection by double clicking or choose the Y Axis
Transform ----- Mark Mirror
Use the selection tool to highlight the triangle.
Transform ------ Reflect
Use the selection tool to deselect the reflected triangle.
Using the selection tool click each point on the relected triangle separately.
Display ----- Show Labels
What happens to the X coordinate, when we reflect in the Y Axis?
Please comment.
Use the selection tool to choose each point on the original and the reflected triangle.
Measure ----- Coordinates
What do you now notice about the x coordinate of the original and the reflected triangle?

Reflection over the X Axis

Launch Geometer's Sketchpad.

Create a new sketch
Under graph in the menu

- select show grid
- snap points.

Using the line segment tool connect points
(-2,1)
(-7,2)
(5,5)
Use the selection tool and click outside the figure which you just created.
Using the selection tool, select each of the three points.
Under display on the menu, choose label points.
Double click the Y axis. This indicates to GPS that you are about to mirror your image over the Y axis.
Use the selection tool to select each of the three points and the three line segments.
Under transform on the menu choose reflect.
Use the selection tool to select the points on the new figure that you just created by reflecting your original figure over the Y axis.
Under display menu choose show labels. Notice that the new labels. The orginal point A now become A prime and the original points B and C also become B and C prime.
What happens to the value of the Y coordinate, when we reflect over the Y axis?

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