TRANSLATIONS
What is a translation in Geometry?
A translation is a transformation that slides every point of a shape the same distance; A transformation that slides a figure along a straight line. The image has the same shape and size as the pre-image.
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; A transformation that flips a figure across a line called the line of reflection. Each point and its image are the same distance from the line of reflection. The image has the same shape and size as the pre-image.
What is a rotation of 90° counterclockwise in the coordinate plane?
A rotation of 90° counterclockwise moves the points in a circular motion around the origin.
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)
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.
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.
To rotate (-3, 4) 270° clockwise, it becomes (-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 the image of (-4, 5) after you translate it right 7 units and down 6 units?
(3, -1)
What is the algebraic rule for a reflection over the x-axis?
(x, y) → (x, -y)
Write the algebraic representation of a 90° rotation counterclockwise of point (x, y).
(x, y) → (-y, x) for 90° counterclockwise.
Why are translations, reflections, and rotations considered rigid transformations?
Because they maintain the original size and shape of the figure.
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.
Does changing the orientation also preserve the congruence of a figure? Justify your answer.
Yes. Changing the orientation is only change the way it faces and keeps the same size and shape of the figure.