TRANSLATIONS
What is a translation in Geometry?
A translation is a transformation that slides every point of a shape the same distance
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?
What does it mean for a transformation to preserve congruence?
It means that the shape and size of the figure remain unchanged. (Same size, same shape)
What do we call the coordinate of a point that has been translated?
A -> ?
A prime
A'
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
One remote interior angle is 38 degrees, and the exterior angle of a triangle is 118 degrees. What is the other remote interior angle?
What is 80 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?
Parallel lines cut by a transversal create obtuse angles and acute angles.
What relationship do all acute angles have?
What relationship do all obtuse angles have?
What relationship do one obtuse and one acute angle have?
all acute angles are equal
all obtuse angle are equal
one obtuse and one acute add to 180 degrees
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)
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 before a transformation.
The two remote interior angles of a triangle are 4x-26 and 5x+3. The exterior angle is 7x+7. What is the value of x?
What is 15?
Describe how translations affect the congruence of shapes.
Translations do preserve congruence because they do not change the size or shape of the figure.
Do reflections preserve congruence? Justify your answer.
Yes, reflections preserve congruence because they do not alter the shape or size of the figure.
How do rotations affect the congruence of shapes?
Rotations preserve congruence because they do not change the size or shape of the figure.
What transformation does not create congruent figures?
Dilation
Enlargement/Shrinking
The only transformation that is NOT a rigid motion that enlarges or shrinks a figure.
What is a dilation?
DAILY DOUBLE!!!
Corresponding angles and alternate interior angles are congruent due to two different transformations. Name the transformations for each.
Corresponding angles -- translations
Alternate Interior Angles -- Rotations