Geometric Transformations: Translations, Rotations, and Reflections Worksheet

Question 1

Point A is at (2, 3). Translate the point 4 units right and 2 units up. What are the new coordinates?

Accepted Answer

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.

Question 2

Point B is at (-1, 5). Translate the point 3 units left and 6 units down. What are the new coordinates?

Accepted Answer

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.

Question 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'?

Accepted Answer

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.

Question 4

Point C is at (3, 2). Rotate the point 90 degrees clockwise around the origin. What are the new coordinates?

Accepted Answer

The new coordinates are (2, -3). A 90 degree clockwise rotation around the origin changes (x, y) to (y, -x).

Question 5

Point D is at (-4, 1). Rotate the point 90 degrees counterclockwise around the origin. What are the new coordinates?

Accepted Answer

The new coordinates are (-1, -4). A 90 degree counterclockwise rotation around the origin changes (x, y) to (-y, x).

Question 6

Point E is at (5, -2). Rotate the point 180 degrees around the origin. What are the new coordinates?

Accepted Answer

The new coordinates are (-5, 2). A 180 degree rotation around the origin changes (x, y) to (-x, -y).

Question 7

Point F is at (6, -3). Reflect the point across the x-axis. What are the new coordinates?

Accepted Answer

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.

Question 8

Point G is at (-2, 7). Reflect the point across the y-axis. What are the new coordinates?

Accepted Answer

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.

Question 9

Point H is at (4, -1). Reflect the point across the line y = x. What are the new coordinates?

Accepted Answer

The new coordinates are (-1, 4). Reflecting across the line y = x switches the x-coordinate and the y-coordinate.

Question 10

A point moves from (1, 4) to (5, 1). Describe the translation in words.

Accepted Answer

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.

Question 11

Point J is at (-3, 2). After a reflection across the y-axis, where is the image point J'?

Accepted Answer

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.

Question 12

Point K is at (2, -5). After a reflection across the x-axis, where is the image point K'?

Accepted Answer

The image point is (2, 5). A reflection across the x-axis keeps the x-coordinate and changes the sign of the y-coordinate.

Question 13

Point L is at (0, 6). Rotate the point 180 degrees around the origin. What are the new coordinates?

Accepted Answer

The new coordinates are (0, -6). A 180 degree rotation changes both coordinate signs, and 0 stays 0.

Question 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.

Accepted Answer

This transformation is a translation. In a translation, every point moves the same distance in the same direction without turning or flipping the shape.

Question 15

A triangle is turned around a fixed point. Is this transformation a translation, rotation, or reflection? Explain.

Accepted Answer

This transformation is a rotation. In a rotation, a figure turns around a fixed point instead of sliding or flipping.

Geometric Transformations: Translations, Rotations, and Reflections

Geometric Transformations: Translations, Rotations, and Reflections

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