Translations & Slides
A transformation that slides every point of a shape the same distance in a given direction without turning or flipping it.
What is a translation?
A rigid motion that flips a figure across a specific line to create a mirror image.
What is a reflection?
True or False: Rigid transformations can change the side lengths or angle measures of a shape.
What is False? (They preserve distance and angle measures).
Performing more than one transformation in a row on a figure is called a sequence of these.
What are transformations?
The point (0,0) on a coordinate plane where the x-axis and y-axis intersect.
What is the origin?
To fully describe a translation, you need to state these two pieces of information.
What are distance and direction? (e.g., 4 units right and 2 units up)
To fully describe a rotation, you need to specify a center point, an angle of rotation, and this.
What is direction? (clockwise or counterclockwise)
The collective term for translations, rotations, and reflections that keep a shape's size and shape unchanged.
What are rigid transformations? (or rigid motions)
Two figures are congruent if there is a sequence of rigid transformations that does this.
What is maps one figure onto the other?
Point Q(-3, -8) lies in this quadrant of the coordinate plane.
What is Quadrant III?
In any transformation, the original shape is called the pre-image, while the resulting shape is called this.
What is the image?
Reflecting the point P(-4, 5) across the x-axis gives these new coordinates for P'.
What is (-4, -5)?
Daily Double: If segment AB is 7 cm long, its length after a 180 degree rotation about a center point.
What is 7 cm?
Point X(1, 2) is translated 3 units right, then reflected across the x-axis. These are the final coordinates.
What is (4, -2)?
If a point at (x, y) is rotated 180 Degree about the origin, these are its new general coordinates.
What is (-x, -y)?
DALIY DOUBLE: On a coordinate grid, if point A(3, -2) is translated 4 units left and 5 units up, these are the coordinates of image A'.
What is (-1, 3)?
Point B(2, -7) is reflected across the y-axis. These are the coordinates of B'.
What is (-2, -7)?
Under rigid transformations, parallel lines always remain this.
What is parallel?
Rotating a figure 90 degree clockwise followed by another 90 degree clockwise rotation is equivalent to a single rotation of this many degrees.
What is 180 degree?
Reflecting a point across the line y = x swaps these two values.
What are the x and y coordinates? (from (x, y) to (y, x))
A point changes from (-2, 5) to (4, 1). Describe the translation.
6 units right and 4 units down.
What is the coordinate rule for a reflection across the x-axis?
What is (x, y) → (x, -y)
A 360 degree rotation about any center point moves a figure to this position.
What is its original position? (or back to itself / the pre-image)
Which transformations preserve congruence: translations, reflections, or rotations?
What is ALL?
Triple Double: Point B(-4, 2) is reflected over the y-axis and then rotated 90° clockwise.
Reflection: (4, 2)