Basic Transformations
This type of transformation slides a figure without turning it.
What is a translation?
The rule (x, y) → (x + 3, y – 2) means the figure moves ___ units right and ___ units down.
What are 3 right and 2 down
A reflection over the x-axis changes the sign of which coordinate?
What is the y-coordinate
Rotate (3, 2) 90° counterclockwise about the origin.
What is (–2, 3)
A dilation with scale factor 2 centered at the origin maps (3, 4) to what point?
What is (6, 8)
A transformation that turns a figure around a fixed point.
What is a rotation
Under (x, y) → (x – 4, y + 1), the point (2, 3) moves to what coordinate?
What is (–2, 4)
Reflect (–3, 5) over the y-axis.
What is (3, 5)
Rotate (–5, 1) 180° about the origin.
What is (5, –1)
A dilation with scale factor ½ reduces the distance between all points by what ratio?
What is ½
A mirror image transformation that flips a figure over a line.
What is a reflection
Translations always produce figures that are ______ to the original.
What is congruent
Reflect (4, –6) over the line y = x.
What is (–6, 4)
Rotate (4, –3) 270° counterclockwise (or 90° clockwise).
What is (–3, –4)
Dilations produce figures that are ______ but not ______ to the original.
What are similar, not congruent
A transformation that changes the size of a figure but keeps the shape the same.
What is a dilation
If a triangle’s vertex moves from (1, 1) to (4, 5), what is the translation rule?
What is (x, y) → (x + 3, y + 4)
A reflection creates a figure that is always ______ to the original.
What is congruent
Which rotation brings (x, y) to (–y, x)?
What is a 90° counterclockwise rotation?
A figure is reflected over the y-axis and then translated 3 units right. What type of transformation is this overall?
What is a composition of transformations
The point about which a figure rotates.
What is the center of rotation?
Translations can change the orientation of a figure.
What is False
Reflect (–2, 3) over the line y = –x.
What is (–3, 2)
True or False: A rotation preserves both size and orientation.
What is True
If a triangle is rotated 90° and then reflected across the x-axis, what has changed: orientation, size, both, or neither?
What is orientation