Rotation 90°CW
Rotate the point A(3, 5) 90° clockwise about the origin.
Answer: A′(5,−3)
Rotate the point A(3, 5) 90° counterclockwise about the origin.
Answer: A′(−5,3)
Rotate the point A(3, 5) 180° about the origin.
Answer: A′(−3,−5)
What movement does a rotation do to a shape?
Answer: It TURNS the shape
Reflect the point (4, -3) over the x-axis
Answer: (4,3)
Rotate the point B(2,0), 90° clockwise about the origin.
Answer: B′(0,−2)
A student rotated the point J(2,–3)J90° counterclockwise and wrote J′(3,2).
THEY'RE CORRECT?
THEY'RE INCORRECT
Answer: (3,2)
What is the rule for a 180° Rotation
Answer
Rule: (x,y)→(−x,−y)
The size changes during a Rotation.
TRUE or FALSE?
Reflect the point Q(−4,2) over the y-axis.
Answer: Q′(4,2)
What is the rule for a 90° Clockwise Rotation?
(x, y) → (y, –x)
What is the rule for a 90° Counterclockwise rotation?
(x, y) → (-y, x)
The point P′ after a 180° rotation is at (6,−2).
a. What were the original coordinates of P before rotation?
Answer: P (-6,2)
How many quadrants do you move with a 90° Rotation?
Answer: 1 quadrant
Dilate the point Q(−6,4)) by a scale factor of 0.5 centered at the origin.
Answer: Q′(−3,2)
A line segment has endpoints L(1,3) and M(4,7).
a. Rotate the segment 90° clockwise about the origin.
Answer:
L′(3,–1),M′(7,–4).
A line segment has endpoints L(1,3) and M(4,7).
a. Rotate the segment 90° counterclockwise about the origin.
Answer:
L′(−3,1),M′(−7,4)
A line segment has endpoints L(-3,3) and M(4,-7).
a. Rotate the segment 180° counterclockwise about the origin.
Answer
L' (3,-3) and M' (-4,7)
Explain the direction for each rotation.
Clockwise
Counter Clockwise
Answer:
Clockwise: Right
Counter Clockwise: Left
Dilate the point P(2,3) by a scale factor of 2 centered at the origin.
Answer: P′(4,6)
The triangle has the following vertices:
P(1,2),Q(3,4),R(2,5).
Rotate the triangle 90° clockwise about the origin.
Answer:
P′(2,−1),Q′(4,−3),R′(5,−2)
Triangle X(–1,2),Y(1,3),Z(0,5)is rotated 90° counterclockwise about the origin.
Answer: X′(–2,–1),Y′(–3,1),Z′(–5,0)
A square has vertices A(0,0),B(2,0),C(2,2),D(0,2).
a. Rotate the square 180° about the origin.
A′(0,0),B′(−2,0),C′(−2,−2),D′(0,−2)
How many quadrants do you move with a 180° Rotation?
Answer:
2 quadrants
Explain how dilating a figure by a scale factor greater than 1 differs from dilating it by a scale factor between 0 and 1.
Answer: A scale factor greater than 1 enlarges the figure (makes it bigger), while a scale factor between 0 and 1 reduces the figure (makes it smaller), but the shape remains similar.