Translations
What is the translation rule for transforming 4 units left and 9 units up?
(x-4, y+9)
What is a reflection over the x-axis?
A reflection over the x-axis flips the shape over the x-axis, changing the sign of the y-coordinate.
What is a rotation of 90° counterclockwise in the coordinate plane?
Turning to the left 1 time.
What does it mean for a transformation to preserve congruence?
It means that the shape and size of the figure remain unchanged. (Rigid)
What is a transversal?
A line that crosses parallel lines.
What do you know about the interior angles of a triangle?
They sum to 180 degrees
The new point (2, 3) translated by 5 units to the right and 2 units up?
The new point would be (7, 5).
If the point (4, -3) is reflected over the y-axis, what are the coordinates of its image?
The coordinates of the image would be (-4, -3).
If the point (1, 2) is rotated 180° around the origin, where is the new position?
The new position would be (-1, -2).
List three transformations that preserve congruence.
Translations, reflections, and rotations.
A rigid motion
A right triangle has one angle that is 30 degrees. What are the other 2 angles?
90 degrees and 60 degrees.
If a shape is translated 3 units left and 4 units down, what is the new position of the vertex (1, 5)?
The new position would be (-2, 1).
What is the algebraic rule for a reflection over the y-axis?
(x, y) → (-x, y)
Explain how you would rotate the point (-3, 4) 270° clockwise and state the new point.
You turn your paper to the right 3 times, the image is at (-4, -3).
Explain how you can determine if two shapes are congruent after a series of transformations.
By checking if all corresponding sides and angles are equal after transformations.
What is a transformation?
Angles that add up to 180 degrees are called ___
supplementary angles
Write the algebraic representation of a translation that moves point (x, y), right 2 units and down 4 units.
(x, y) → (x + 2, y - 4)
DAILY DOUBLE!!!
What is the algebraic rule for a reflection over the x-axis?
(x, y) → (x, -y)
What word can you use to describe a rotation? [other than rotate]
Turn
Spin
Why are translations, reflections, and rotations considered rigid motions?
Because they maintain the original size and shape of the figure.
The figure after a transformation is called______
An image
What are vertical angles and what is true about their measurements?
They are opposite angles and they are equal.