Exploring rotations worksheet :
Worksheet given in this section would be much useful to the students who would like to practice problems on "Rotations".
1. The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° counterclockwise about the origin and write the vertices of the image.
2. The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° clockwise about the origin and write the vertices of the image.
3. Based on the rotation in question 1, write the general rule for 90° counterclockwise rotation about the origin.
4. Based on the rotation in question 2, write the general rule for 90° clockwise rotation about the origin.
5. How are the size and the orientation of the triangle affected by the rotation ?
Question 1 :
The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° counterclockwise about the origin and write the vertices of the image.
Answer :
Step 1 :
Trace triangle xyz and the x- and y-axes onto a piece of paper.
Step 2 :
Rotate your triangle 90° counterclockwise about the origin. The side of the triangle that lies along the x-axis should now lie along the y-axis.
Step 3 :
Sketch the image of the rotation. Label the images of points X, Y, and Z as X', Y', and Z'.
Step 4 :
Write the vertices of the image x'y'z'.
X'(0, 0), Y'(0, 2) and Z'(-4, 2)
Question 2 :
The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° clockwise about the origin and write the vertices of the image.
Answer :
Step 1 :
Trace triangle xyz and the x- and y-axes onto a piece of paper.
Step 2 :
Rotate your triangle 90° clockwise about the origin. The side of the triangle that lies along the x-axis should now lie along the y-axis.
Step 3 :
Sketch the image of the rotation. Label the images of points X, Y, and Z as X", Y", and Z".
Step 4 :
Write the vertices of the image x"y"z".
X"(0, 0), Y"(0, -2) and Z"(4, -2)
Question 3 :
Based on the rotation in question 1, write the general rule for 90° counterclockwise rotation about the origin.
Answer :
X(0, 0) -------> X'(0, 0)
Y(2, 0) -------> Y'(0, 2)
Z(2, 4) -------> Z'(-4, 2)
From the above transformations of vertices, we have the following general rule for 90° counterclockwise rotation.
Pre-image (x, y) |
Image (After rotation) (-y, x) |
Question 4 :
Based on the rotation in question 2, write the general rule for 90° clockwise rotation about the origin.
Answer :
X(0, 0) -------> X"(0, 0)
Y(2, 0) -------> Y"(0, -2)
Z(2, 4) -------> Z"(4, -2)
From the above transformations of vertices, we have the following general rule for 90° clockwise rotation.
Pre-image (x, y) |
Image (After rotation) (y, -x) |
Similarly, we can define general rules for clockwise and counterclockwise rotations about 180°and 270° as given below.
Question 5 :
How are the size and the orientation of the triangle affected by the rotation ?
Answer :
The size stays the same, but the orientation changes in that the triangle is turned or tilted left – what was “up” is now “left”.
After having gone through the stuff given above, we hope that the students would have understood "Rotations".
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