Transformations: Translations, Rotations, Reflections Worksheet

Question 1

Point A is located at (2, 3). Translate point A 4 units right and 2 units down. What are the coordinates of A'?

Accepted Answer

The coordinates of A' are (6, 1). Moving 4 units right adds 4 to the x-coordinate, and moving 2 units down subtracts 2 from the y-coordinate.

Question 2

Triangle ABC has vertices A(1, 1), B(4, 1), and C(2, 3). Translate the triangle 3 units left and 5 units up. Write the coordinates of A', B', and C'.

Accepted Answer

The translated coordinates are A'(-2, 6), B'(1, 6), and C'(-1, 8). Each x-coordinate decreases by 3, and each y-coordinate increases by 5.

Question 3

A point P(-3, 5) is reflected across the x-axis. What are the coordinates of P'?

Accepted Answer

The coordinates of P' are (-3, -5). A reflection across the x-axis keeps the x-coordinate the same and changes the sign of the y-coordinate.

Question 4

A point Q(6, -2) is reflected across the y-axis. What are the coordinates of Q'?

Accepted Answer

The coordinates of Q' are (-6, -2). A reflection across the y-axis changes the sign of the x-coordinate and keeps the y-coordinate the same.

Question 5

Rectangle WXYZ has vertices W(-1, 2), X(3, 2), Y(3, -1), and Z(-1, -1). Reflect the rectangle across the x-axis. Write the coordinates of W', X', Y', and Z'.

Accepted Answer

The reflected coordinates are W'(-1, -2), X'(3, -2), Y'(3, 1), and Z'(-1, 1). Each x-coordinate stays the same, and each y-coordinate changes sign.

Question 6

Point R(4, 7) is rotated 90 degrees counterclockwise about the origin. What are the coordinates of R'?

Accepted Answer

The coordinates of R' are (-7, 4). A 90 degree counterclockwise rotation about the origin changes (x, y) to (-y, x).

Question 7

Point S(-2, 5) is rotated 180 degrees about the origin. What are the coordinates of S'?

Accepted Answer

The coordinates of S' are (2, -5). A 180 degree rotation about the origin changes (x, y) to (-x, -y).

Question 8

Point T(-6, -1) is rotated 90 degrees clockwise about the origin. What are the coordinates of T'?

Accepted Answer

The coordinates of T' are (-1, 6). A 90 degree clockwise rotation about the origin changes (x, y) to (y, -x).

Question 9

A figure has vertices A(2, 1), B(5, 1), and C(5, 4). Reflect the figure across the y-axis. Then translate it 2 units right. Write the final coordinates of A'', B'', and C''.

Accepted Answer

After reflecting across the y-axis, the coordinates are A'(-2, 1), B'(-5, 1), and C'(-5, 4). After translating 2 units right, the final coordinates are A''(0, 1), B''(-3, 1), and C''(-3, 4).

Question 10

A shape is moved so that every point shifts 7 units left and 3 units up. What type of transformation is this, and does the shape change size or orientation?

Accepted Answer

This transformation is a translation. The shape does not change size or orientation because every point moves the same distance in the same direction.

Question 11

A triangle is flipped over the line y = 0. What type of transformation is this, and what is another name for the line y = 0?

Accepted Answer

This transformation is a reflection. The line y = 0 is the x-axis, so the triangle is reflected across the x-axis.

Question 12

Point M(3, -4) is transformed to M'(-3, -4). Identify the transformation.

Accepted Answer

The transformation is a reflection across the y-axis. The x-coordinate changed sign from 3 to -3, and the y-coordinate stayed the same.

Question 13

Point N(2, 6) is transformed to N'(-6, 2). Identify the rotation about the origin.

Accepted Answer

The transformation is a 90 degree counterclockwise rotation about the origin. The rule (x, y) becomes (-y, x), so (2, 6) becomes (-6, 2).

Question 14

Parallelogram ABCD has vertices A(-4, -2), B(-1, -2), C(0, 1), and D(-3, 1). Rotate the parallelogram 180 degrees about the origin. Write the coordinates of A', B', C', and D'.

Accepted Answer

The rotated coordinates are A'(4, 2), B'(1, 2), C'(0, -1), and D'(3, -1). A 180 degree rotation about the origin changes each coordinate pair (x, y) to (-x, -y).

Question 15

A point starts at (1, -3). It is translated 5 units up, reflected across the y-axis, and then rotated 180 degrees about the origin. What are the final coordinates?

Accepted Answer

After translating 5 units up, the point is (1, 2). After reflecting across the y-axis, the point is (-1, 2). After rotating 180 degrees about the origin, the final coordinates are (1, -2).

Transformations: Translations, Rotations, Reflections

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