Geometric Transformations: Translations, Rotations, and Reflections
Describe and apply basic transformations on the coordinate plane
Geometric Transformations: Translations, Rotations, and Reflections
Describe and apply basic transformations on the coordinate plane
Math - Grade 6-8
- 1
Point A is at (2, 3). Translate the point 4 units right and 2 units up. What are the new coordinates?
Right changes x positively, and up changes y positively.
The new coordinates are (6, 5). Moving 4 units right adds 4 to the x-coordinate, and moving 2 units up adds 2 to the y-coordinate. - 2
Point B is at (-1, 5). Translate the point 3 units left and 6 units down. What are the new coordinates?
The new coordinates are (-4, -1). Moving 3 units left subtracts 3 from the x-coordinate, and moving 6 units down subtracts 6 from the y-coordinate. - 3
Triangle ABC has vertices A(1, 1), B(4, 1), and C(2, 3). Translate the triangle by the rule (x, y) to (x + 2, y - 1). What are the new coordinates of A', B', and C'?
Apply the same rule to each vertex.
The new coordinates are A'(3, 0), B'(6, 0), and C'(4, 2). The rule adds 2 to each x-coordinate and subtracts 1 from each y-coordinate. - 4
Point C is at (3, 2). Rotate the point 90 degrees clockwise around the origin. What are the new coordinates?
The new coordinates are (2, -3). A 90 degree clockwise rotation around the origin changes (x, y) to (y, -x). - 5
Point D is at (-4, 1). Rotate the point 90 degrees counterclockwise around the origin. What are the new coordinates?
For a 90 degree counterclockwise rotation, switch the coordinates and change the sign of the new x-value.
The new coordinates are (-1, -4). A 90 degree counterclockwise rotation around the origin changes (x, y) to (-y, x). - 6
Point E is at (5, -2). Rotate the point 180 degrees around the origin. What are the new coordinates?
The new coordinates are (-5, 2). A 180 degree rotation around the origin changes (x, y) to (-x, -y). - 7
Point F is at (6, -3). Reflect the point across the x-axis. What are the new coordinates?
A reflection across the x-axis flips a point up or down.
The new coordinates are (6, 3). Reflecting across the x-axis keeps the x-coordinate the same and changes the sign of the y-coordinate. - 8
Point G is at (-2, 7). Reflect the point across the y-axis. What are the new coordinates?
The new coordinates are (2, 7). Reflecting across the y-axis keeps the y-coordinate the same and changes the sign of the x-coordinate. - 9
Point H is at (4, -1). Reflect the point across the line y = x. What are the new coordinates?
Points reflected across y = x trade places between x and y.
The new coordinates are (-1, 4). Reflecting across the line y = x switches the x-coordinate and the y-coordinate. - 10
A point moves from (1, 4) to (5, 1). Describe the translation in words.
The translation is 4 units right and 3 units down. The x-coordinate increases from 1 to 5, and the y-coordinate decreases from 4 to 1. - 11
Point J is at (-3, 2). After a reflection across the y-axis, where is the image point J'?
The image point is (3, 2). A reflection across the y-axis changes the sign of the x-coordinate and leaves the y-coordinate unchanged. - 12
Point K is at (2, -5). After a reflection across the x-axis, where is the image point K'?
The point stays the same distance from the x-axis.
The image point is (2, 5). A reflection across the x-axis keeps the x-coordinate and changes the sign of the y-coordinate. - 13
Point L is at (0, 6). Rotate the point 180 degrees around the origin. What are the new coordinates?
The new coordinates are (0, -6). A 180 degree rotation changes both coordinate signs, and 0 stays 0. - 14
A shape is moved so that every point shifts the same distance in the same direction. Is this transformation a translation, rotation, or reflection? Explain.
Think about a shape sliding across the plane.
This transformation is a translation. In a translation, every point moves the same distance in the same direction without turning or flipping the shape. - 15
A triangle is turned around a fixed point. Is this transformation a translation, rotation, or reflection? Explain.
This transformation is a rotation. In a rotation, a figure turns around a fixed point instead of sliding or flipping.