Rigid Transformation
True or False:
A rigid transformation changes the size after a transformation.
False
Be ready to justify :)
True or False:
Translating a figure 4 units left and 3 units up changes the size of the figure
False. A translation changes the position but preserves the size and shape so it can remain congruent.
Reflect A(-2,-4) over the y-axis to form A',
A' (-2,4)
Rotate B(2,-3) 90 degrees clockwise to form B'.
B'( -3,-2)
A''' (A triple prime)
How many degrees is each quadrant?
90
Translate (4,8) 2 units up
(4,10)
Triangle ABC has A(2,1),B(5,1),C(2,4). The triangle is reflected across the y-axis. What are the coordinates of the new triangle?
A′(−2,1),B′(−5,1),C′(−2,4)
Rotate (5,-4) 270 degrees counterclockwise
(-4,-5)
Point A(2,−3) is translated 4 units right and 5 units up. What are the coordinates of A′?
(6,2)
Which of the following is NOT a rigid transformation?
A. Translation
B. Reflection
C. Rotation
D. Dilation
D. Dilation
Translate (-3,-4) 7 units to the right
(4,-4)
Point P(6,−3) is reflected to P′(−6,−3). Across which axis was the point reflected? Explain how you know.
The y-axis. The x-coordinate changes sign while the y-coordinate stays the same. QIV to QIII
Point P(5,−2) is rotated 180° about the origin. A student says the answer is (−5,−2). Is the student correct? Explain.
No. A 180° rotation changes both coordinates signs but doesn't turn the numbers, so the correct answer is (−5,2). Q4 takes two right turns and the image will be in Q2.
P(-4,4) Q(-2,3) R(-5,2) is reflected across the x-axis and rotated 180 clockwise. What is P''Q''R''?
P''(4,4) Q''(2,3) R''(5,2)
Triangle ABC is transformed into triangle A'B'C'. Before the transformation, AB=7 units and BC=5 units. After the transformation, A′B′=7 units and B′C′=5 units. Is this a rigid transformation?
Yes because rigid transformations preserves distances/side lengths
Triangle J(-4,5) K(-2,1) L (-4,2) is translated 6 units to the right. What is triangle J'K'L' coordinates?
J'(2,5) K'(4,1) L'(2,2)
What are the coordinates of the point (x,y) when it is reflected across the x-axis?
(x,-y)
Triangle ABC has vertices A(1,2),B(4,2),C(1,5). The triangle is rotated 90° clockwise about the origin. Find the coordinates of all three vertices after the rotation.
A′(2,−1),B′(2,−4),C′(5,−1)
Triangle A(1,1) B(1,3) C(4,1) translates 6 units to the left then reflects across the y-axis. What is A''B''C''?
A''(5,1) B''(5,3) C''(2,1)
A (-5,-2) B (-3,-1) C(-1,-1) D (-3,-4) goes through a single transformation to form A'(2,-2) B'(4,-1) C'(6,-1) D'(4,-4). What is the single transformation?
Translation 7 units to the right
Point P(5,−2) is translated to P′(−1,4). Describe the translation that was performed.
6 units left and 6 units up
Reflect figure A(-3,4) B(-1,4) C(-2,1) D(-4,3) across the x-axis. What is A'B'C'D?
A'(-3,-4) B'(-1,-4) C'(-2,-1) D' (-4,-3)
Triangle ABC rotates from A(-4,4) B(-3,5) C(-1,3) to A'(-4,-4) B'(-5,-3) C' (-3,-1). What single rotation maps triangle ABC onto A'B'C?
270clockwise or 90 counterclockwise
A triangle has vertices A(1,1),B(4,1),C(1,3). The triangle is reflected across the y-axis and then translated 5 units right. What are the coordinates of the final triangle?
A''(4,1),B''(1,1),C''(4,3)