ROTATION 9-3
Before rotating any figure you need to know the center of rotation, the angle of rotation, and whether the rotation is clockwise or counterclockwise. Just for our purposes the figure will be rotated counterclockwise unless stated otherwise.
Now I am going to show you a step-by-step method on how to rotate a figure counterclockwise around a point with a set number of degrees.
1. Place your protractor on point C (Center of Rotation), and then make a 100-degree angle from any point on the figure. It may be easier to make a line form the chosen point to point C. I choose the point O to make my 100-degree angle, then made an ray from point C.
2. Using your compass measure line CO and then with the same measurement mark an ark on ray C. The intersection between the ray and the ark is O’. This is the 100-degree rotation of point O counterclockwise.
3. Now repeat at for every point on the figure so that the whole figure will be rotated 100-degrees.
All regular polygons have a center that is equidistant from its vertices. The segments that connect the center of the polygon to all of its vertices make congruent triangles in the polygon. Those triangles can help find the rotation image if the center was the center for rotation.
1. First you find out the measure of degree each triangle is.
2. Then by looking you can see how many triangles the pre-image went over.
3. Then multiply the degree of the triangle by the number of triangles the pre-image went over to find the image.
Here is a great practice problem for centers!
Answers: 10. H
11. M
12. C
13. BC
14. A
15. ML
16. I
17. J
Symmetry 9-4
Line Symmetry – One half of the figure is a mirror image of its other half. Fold the figure along the line of symmetry and the halves match exactly.
Rotational Symmetry – the same image for some rotation of 180-degree or less turn.
Point Symmetry – has a 180-degree rotational symmetry.
Try this out!
Answer: 17. Line Symmetry and Rotational Symmetry.
18. Line Symmetry