Translations
Reflections
Rotations
Congruence and Similarity
Transformations Challenge
100
True or False:
FRI-YAYs are FANTASTIC
100% True
100
What is a reflection in geometry?
A reflection is a transformation that flips a figure over a line, creating a mirror image.
100
What is a rotation in geometry?
A rotation is a transformation that turns a figure around a fixed point, called the center of rotation.
100
What does it mean for two figures to be congruent?
Two figures are congruent if they have the same shape and size, but their positions may differ.
100
Name a transformation that preserves both the size and the shape of a figure.
A rigid transformation, such as a translation, rotation, or reflection.
200
Describe what happens to the coordinates of a point (x,y) when translated 5 units up.
The y-coordinate increases by 5, so the new coordinates are (x,y+5).
200
Describe what happens to the coordinates of a point (x,y)(x, y)(x,y) when it is reflected over the x-axis.
The y-coordinate is negated, so the new coordinates are (x,−y)
200
Describe what happens to the coordinates of a point (x,y) when rotated 90 degrees counterclockwise about the origin.
The new coordinates are (−y,x)
200
What does it mean for two figures to be similar?
Two figures are similar if they have the same shape but not necessarily the same size, and their corresponding angles are equal and sides proportional.
200
A figure is translated, then reflected, and then rotated. Does the order of these transformations matter for the final image? Explain briefly.
Yes, the order matters because performing these transformations in a different sequence can lead to a different final image.
300
If a figure is translated left by 4 units and down by 3 units, how do the coordinates of a point (x,y) change?
The x-coordinate decreases by 4 and the y-coordinate decreases by 3, so the new coordinates are (x−4,y−3)
300
How do the coordinates of a point (x,y) change when reflected over the y-axis?
The x-coordinate is negated, so the new coordinates are (−x,y)
300
What are the coordinates of a point (2,−5) after a 180-degree rotation about the origin?
The new coordinates are (−2,5)
300
True or False: A rotation always preserves the shape and size of a figure.
True.
300
What type of transformation(s) can be used to map a shape onto itself?
Identity transformation or a 360-degree rotation
400
A point at (3,−2)(3, -2)(3,−2) is translated to (−2,−5)(-2, -5)(−2,−5). How many units right/left and up/down was it moved?
The point moved 5 units left and 3 units down.
400
A point (4,3) is reflected over the y-axis. What are the coordinates of the reflected point?
The coordinates are (−4,3)
400
A triangle has vertices at (1,3), (4,3), and (2,1). What are the new coordinates of the vertices if rotated 270 degrees clockwise about the origin?
The new coordinates are (3,−1), (3,−4), and (1,−2)
400
These two triangles are congruent. Create an accurate congruency statement.
Triangle STR is congruent to Triangle EDF
400
Describe a sequence of transformations that would map a triangle at (1,2), (3,5), and (6,1) to (−1,−2), (−3,−5), and (−6,−1).
A 180-degree rotation about the origin.
500
If a triangle is translated so that the new coordinates are (x+7,y−2), what direction and how far has the triangle been translated?
The triangle was translated 7 units to the right and 2 units down.
500
If a figure is reflected across the line y=x, what happens to the coordinates of each point on the figure?
The coordinates switch places, so (x,y) becomes (y,x)
500
Explain how you would determine the coordinates of a point (x,y) after a 360-degree rotation about the origin.
The coordinates remain the same, (x,y), because a 360-degree rotation brings the figure back to its original position.
500
If two figures are similar, what does this tell you about their corresponding sides and angles?
Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.
500
Explain how you can use a series of transformations to show that two figures are similar but not congruent.
Use a dilation (which changes the size) combined with rigid transformations (translations, rotations, or reflections) to map one figure onto the other, showing they are similar but not congruent.