Rotations and dilations

1. Transformations
ROTATIONS AND DILATIONS

2. What is a rotation?
 Rotation means turning around a center
 The distance from the center to any point on the shape stays the same.
 Every point makes a circle around the center.
 Check out my source for a neat GIF that shows a rotation.
 Source: http://www.mathsisfun.com/geometry/rotation.html

3. Rotation Tricks
 If your original point A (x , y) is rotated 90° counterclockwise it becomes
A’(-y , x).
 If your original point B (x, y) is rotated 90° clockwise it becomes B’(y, -x)
 If your original point C (x, y) is rotated 180° counterclockwise or clockwise it
becomes (-x, -y). (if you go 180° in counterclockwise or clockwise they
would both end up in the same place)
 If your original point D (x, y) is rotated 270° counterclockwise it becomes
D’(y, -x). (Same as 90° clockwise)

4. Try These…
 Rotate Q (-1, 3) 90° counterclockwise about the origin.
 Rotate M(4, -6) 270° counterclockwise about the origin.
 Rotate N (-2, -3) 180° clockwise about the origin.
 Rotate Triangle T (0, -9) U (7, 8) V (-6, 3) 90° clockwise about the origin.

5. Answers….
 Q’ (-3, -1)
 M’ (-6, -4)
 N’ (2, 3)
 T’(-9, 0) U’(8, -7) V’(3, 6)
 This is a great site that has more practice if you need it! It will really help
you with the Mastery Assignment.
http://www.ixl.com/math/geometry/rotations-find-the-coordinates

6. Dilations
 A dilation stretches or shrinks an object. It is the same shape as the original,
just a different size.
 The scale factor is how much the object stretches or shrinks.
 If the scale factor is greater than one, the object stretches. If it between
zero and 1 (0<k<1) then the object shrinks.
 To find the new image, simply multiply the points by the scale factor.
 Source:
http://www.regentsprep.org/regents/math/geometry/gt3/ldilate2.htm

7. Try some…
 Triangle A (-2, 3) B(3, 6) C (-5, 9) is dilated by a scale factor of ½. Find the
new points of the image.
 Triangle Q (4, -1) R (-4, 8) S (10, 2) is dilated by a scale factor of 3. Find the
new points of the image.
 Triangle D (-3, -4) E (6, 8) F (12, 2) is dilated and is now at D’ (-6, -8) E’ (12,
16) F’ (24, 12). By what scale factor did the dilation occur?

8. Answers…
 A’ (-1, 1.5) B’ (1.5, 3) C’ (-2.5, 4.5)
 Q’ (12, -3) R’ (-12, 24) S’ (30, 6)
 Scale factor = 2
 Need some extra practice to get ready for the mastery assignment?
http://www.ixl.com/math/grade-8/dilations-find-the-coordinates