Transformations
This transformation is also known as a slide.
What is a translation?
Reflect the point (1, 3) across the x-axis.
(1, -3)
Translate the point (-2, -3) by (x, y) --> (x + 2, y - 1).
(0, -4)
Rotate the point (2, -1) 90 degrees clockwise around the origin.
(-1, -2)
Triangle ABC is translated and the image is labeled DEF. Triangle DEF is then rotated and the new image is labeled GHI. Which point in triangle GHI is the image of point C?
Point I
This transformation is also called a flip.
What is a reflection?
Reflect the line segment from (-2, 1) to (-3, -3) across the y-axis.
(2, 1) to (3, -3)
Translate the line segment with endpoints at (1, -3) and (-2, 3) by (x, y) --> (x – 2, y – 2).
(-1, -5) to (-4, 1)
Rotate the line segment with endpoints at (3, -3) and (-2, 1) 90 degrees counterclockwise around the origin.
(3, 3) to (-1, -2)
Reflect the point (3, -2) across the x-axis and then translate it by (x, y) --> (x – 1, y +1).
(2, 3)
This transformation is also known as a turn.
What is a rotation?
Reflect the triangle with vertices at (3, -2), (-4, 3) and (-2, -2) across the x-axis.
(3, 2), (-4, -3) and (-2, 2)
Translate the triangle with vertices at (2, 3), (4, 3) and (-1, -2) by (x, y) --> (x + 2, y – 2).
(4, 1), (6, 1) and (1, -4)
Rotate the triangle with vertices at (0, 3), (2, -1) and (-1, -3) 180 degrees around the origin.
(0, -3), (-2, 1) and (1, 3)
Translate the point (-1, -1) by (x, y) --> (x – 2, y -1) and then rotate the image by 90 degrees counterclockwise around the origin.
(2, -3)
Riding on an escalator is an example of this kind of transformation.
What is a translation?
Reflect the triangle with vertices at (0, 0), (2, 2) and (-1, -3) across the y-axis.
(0, 0), (-2, 2), and (1, -3)
Translate the triangle with vertices at (1, 1), (-2, 2) and (3, -1) by (x, y) --> (x + 4, y + 0).
(5, 1), (2, 2) and (7, -1)
Rotate the triangle with vertices at (0, 0), (-2, -3) and (1, 1) 90 degrees counterclockwise around the origin.
(0, 0), (3, -2) and (-1, 1)
Rotate the point (3, -2) by 180 degrees around the origin and then reflect the image across the y-axis.
(3, 2)
This kind of transformation can be done around the origin or around another point.
What is a rotation?
Reflect the triangle with vertices at (2, 1), (3, 2) and (5, -2) across the line x = 1.
(0, 1), (-1, 2) and (-3, -2)
Translate the triangle with vertices at (0, 2), (2, 0) and (-3, -3) two units down and four units right.
(4, 0), (6, -2) and (1, -5)
Rotate the triangle with vertices at (2, 0), (2, 3) and (0, 3) 180 degrees around the point (2, 0).
(2, 0), (2, -3) and (4, -3)
Reflect the point (-5, 1) across the x-axis, then translate the image by (x, y) (x + 1, y - 2), then rotate the new image by 90 degrees clockwise around the origin.
(-3, 4)