Rotation
What is a rotation?
A rotation is a transformation in which the object is rotated about a fixed point. The direction of rotation can be clockwise or counterclockwise.
What is a translation?
A translation is when a figure is moved from one location to another location without changing its size, shape, or orientation.
What is a dilation?
A transformation that changes the size of a figure, but not the shape.
What is a reflection?
A reflection is the flipping of a point or figure over a line of reflection (mirrored image)
What are the rotation coordinates for
90° CW/CCW
270° CW/CCW
180° CW/CCW
90° CW/270° CCW: (y,-x)
90° CCW/270° CW: (-y,x)
180° CW/CCW: (-x,-y)
True or false?
Translations are non-rigid
False
Translations are rigid
What is scale factor?
The ratio used to enlarge or reduce a figure.
1. Reflection over the y-axis goes from (x,y) to ____
2. Reflection over the x-axis goes from (x,y) to ____
1. (-x,y)
2. (x,-y)
What is the new point of (1,8) after a rotation of 180° counterclockwise about the origin?
A) (-1,8)
B) (8,-1)
C) (8,1)
D) (-1,-8)
D) (-1,-8)
What happened to these two points?
Before: (3,7) (3,9)
After: (-2,-2) (-2,0)
The two coordinates are translated 5 units to the left and 9 units down
True or Flase?
A dilation applies to both horizontal and vertical components.
True
A dilation applies to both horizontal and vertical components.
1. Reflection over y=x goes from (x,y) to _____
2. Reflection over y=-x goes from (x,y) to _____
1. (y,x)
2. (-y,-x)
What is the new point if (3,-2) rotates 90° counterclockwise about the origin?
(2,3)
ABC is translated 2 units right and 4 units up what are the new coordinates.
A: (-8,-1) B: (-3,-1) C: (-6,-5)
A: (-6,3) B: (-1,3) C: (-4,-1)
1. A scale factor greater than 1 means _____
2. A scale factor less than 1 means _____
1. Enlargment to the figure
2. Reduction to the figure
(7,5) reflected over y=-x is
A) (7,5)
B) (-5,-7)
C) (5,7)
D) (-7,5)
B) (-5,-7)
The coordinates trade places and sign change
If you rotate the point (4,2) 90 degrees counterclockwise and then rotate it again, 180 degrees clockwise. What will the new point be?
(2,-4)
If (3,5) is moved 3 units left, 2 units up, and the 5 units right. What is the new coordinate?
A) (5,7)
B) (4,7)
C) (-4,5)
A) (5,7)
Determine the coordinates of ABC and A1 B1 C1 and find the scale factor.
A (2,1) A1 (6,3)
B (5,1) B1 (15,3)
C (2,6) C1 (9,18)
Scale factor = 3
(2,1) x3 (6,3)
(5,1) x3 (15,3)
(3,6) x3 (9,18)
If you reflect A, B, C, and D over the y-axis what are your points now?
Original points:
A (-2,2) B (-2,6) C (-6,2) D (-6,6)
A (2,2) B (2,6) C (6,2) D (6,6)