Rigid Transformations
To "flip" a figure.
Reflection
True or False? Dilations always make a figure smaller.
False
Is a dilation of 1.5 an enlargement or reduction?
Enlargement (Gets bigger)
Segment AB is dilated from center O by a scale factor of 3. If the length of AB is 4, what is the length of A'B'?
If triangle ABC is dilated from the origin and A(2 , 5), what would the coordinates of A' be if the scale factor was 4?
A'(8 , 20)
To "slide" a figure.
Translation
A dilation might change the size of a figure's side lengths but never the _______.
angles
If triangle ABC is dilated by a scale factor of 4 and the measure of angle B is 36 degrees, what will the measure of angle B' equal and why? (Must explain your reasoning).
The measure of angle B' would also be 36 degrees because dilations preserve the measures of angles.
If segment KJ is dilated from center O by a scale factor of 1/2 and the length of K'J' is 10 cm, what is the length of KJ?
The length of KJ is 20 cm.
Vertex X of triangle XYZ has coordinates (-4 , 10). What are the coordinates of X' under a dilation centered at the origin with a scale factor of 1/2?
X'(-2 , 5)
To "turn" a figure.
Rotation
Dilations always produce ___________ figures.
similar
If the scale factor is greater than 1 (ex:2) then the dilated image is ______________ from the original figure.
Enlarged
A circle is dilated by a scale factor of 4.26 cm. If the diameter of the circle is 8 cm what is the radius of the dilated circle?
The radius of the dilated circle is 17.04 cm
Triangle A'B'C' is the image of triangle ABC under a dilation centered at O. If AB = 11, BC = 8, A'B' = 41.8 and B'C' = 30.4, what is the scale factor?
The scale factor would be 3.8
Describing a translation requires these two things.
1) Direction
2) Distance
Dilations need these two things.
1) Center Point of Dilation
2) Scale Factor
If the scale factor is less than 1 (ex:1/4) then the dilated image is ____________ from the original figure.
Reduced
Segment AR is 14.2 mm. If segment A'R' is 113.6 mm, what is the scale factor?
The scale factor is 8.
Vertex O of triangle DOG has coordinates (-3 , 6). If triangle DOG is dilated with center of dilation at the origin and O' has coordinates (-12 , 24), what is the scale factor?
The scale factor is 4
Describing a rotation requires these three things.
1) Center (Point)
2) Rotation angle (Degrees)
3) Direction (Clockwise or Counterclockwise)
How will dilating a figure with a scale factor of 1/3 change a figure? How many times bigger or smaller will it get?
It will make the figure 3 times smaller from the center of dilation.
Dilations can result in a congruent figure if their scale factor is this number.
1
Polygon ABCDE is dilated from center O. If CD = 22.8 inches and C'D' = 5.7 inches, what is the scale factor?
The scale factor is 1/4 (or 0.25)
Vertex C of figure CARE has the coordinates (p , t). What are the coordinates of vertex C' under a dilation centered at the origin with scale factor 3/7?
C'((3/7)p , (3/7)t)