Transformations Task III – Counterclockwise Rotations
Part B
Name ______
We will be looking at rotations of figures and how they work. A rotation is a transformation that turns a figure about a fixed point for a given angle, called the angle of rotation and a given direction. The angle of rotation is the amount of rotation about a fixed point or point of rotation. Rotations can be performed in a clockwise or counterclockwise direction.
In the following activity ALL of the rotations will be performed in the COUNTERCLOCKWISE direction about the point of origin.
1.Explain in your own words what the sentence above means.
2.Draw a right triangle using the coordinate pairs A(8,1), B(8,6), C(2,6). Be sure to label each vertex with the correct letter and connect the points.
3.Record the coordinates of each vertex in the column that is labeled 0°.
4.Now you are ready to perform you first rotation. Rotate the transparency 90° counterclockwise and record the coordinates of the vertices for new figure in the column labeled 90°.
5.Rotate the transparency back to the original position.
6.From the original figure, rotate the transparency 180° counterclockwise and record the coordinates of the vertices for new figure in the column labeled 180°.
7.Rotate the transparency back to the original position.
8.From the original figure, rotate the transparency 270° counterclockwise and record the coordinates of the vertices for new figure in the column labeled 270°.
9.Rotate the transparency back to the original position.
10.From the original figure rotate the transparency 360° and record the coordinates of the vertices for new figure in the column labeled 360°.
11.Using the coordinates from your table draw each new figure on the graph provided. Be sure to label each vertex (A,B,C) along with the appropriated prime markings.
COUNTERCLOCKWISEROTATIONS RECORD TABLE
Triangle Vertices / 0° Rotation / 90° Rotation / 180° Rotation / 270° Rotation / 360° RotationA
B
C
12.Describe what pattern you notice in how the coordinates changed when the figure was rotation from 0° to 90°.
13.Describe what pattern you notice in how the coordinates changed when the figure was rotation from 0° to 180°.
14.Describe what pattern you notice in how the coordinates changed when the figure was rotation from 0° to 270°.
15.Describe what pattern you notice in how the coordinates changed when the figure was rotation from 0° to 360°.
16.Did the size of the shape change after any of the rotations? Explain why or why not.
17.Use the Cartesian graph above and plot and connect the points
A(-2,2), B(-2,7), C(1,7), D(1,4), E(3,4), F(3,2). Label each vertex.
18.What will the new ordered pairs be if you rotate the figure 90° clockwise? Explain your reasoning.
19.What will the new ordered pairs be if you rotate the figure 90° counterclockwise? Explain your reasoning.
20.Would the (x,y) be the same for a figure rotated 90° clockwise as it would be for a figure rotated 270° counterclockwise? Use the graph and figure above to prove your argument.