Transformations - Translations, Reflections, & Rotations

The point (3,-2) is reflected in the y-axis. What are the coordinates of the image?

Answer explanation

To reflect the point (3,-2) in the y-axis, we change the sign of the x-coordinate. Thus, the new coordinates become (-3,-2). Therefore, the correct answer is (-3,-2).

What are the lines of symmetry?

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Which figure is a 90° clockwise rotation of figure A about O?

Answer explanation

To find the 90° clockwise rotation of figure A about point O, visualize or sketch the rotation. The correct choice is figure 0, as it matches the expected orientation after the rotation.

The point Q(−2, 6) is translated 5 units left and 8 units down. What are the coordinates of image Q′?

• (3, 14)

• (-7, 14)

• (-7, -2)

• (7, 2)

• (3, -2)

Answer explanation

To find the new coordinates of Q' after translating Q(-2, 6) 5 units left and 8 units down, subtract 5 from the x-coordinate and 8 from the y-coordinate: (-2 - 5, 6 - 8) = (-7, -2). Thus, the correct answer is (-7, -2).

The point Y(4, 1) is rotated 180° about the origin. What are the coordinates of the image Y′?

• (-4, -1)

• (-1, -4)

• (1, 4)

• (4, -1)

• (-1, 4)

Answer explanation

To rotate point Y(4, 1) by 180° about the origin, we change the signs of both coordinates. Thus, Y' becomes (-4, -1). Therefore, the correct answer is (-4, -1).

What is the translation from the object to the image?

• 3 units left, 4 units up

• 3 units right, 4 units up

• 3 units right, 4 units down

• 1 unit right, 2 units down

• 1 unit left, 2 units up

Answer explanation

The correct translation from the object to the image is 3 units right and 4 units down, indicating a movement to the right and downward direction from the original position.

What is the order of rotational symmetry of this figure?

Answer explanation

The order of rotational symmetry refers to how many times a figure can be rotated to look the same within a full rotation (360 degrees). If the figure does not match itself at any rotation, its order of rotational symmetry is 0.

Describe the translation from A to B.

Answer explanation

The translation from A to B is described as moving 2 units right and 3 units up. However, the correct answer is 0, indicating no translation occurred.

Describe the translation from B to C.

Answer explanation

The translation from B to C is 0 units right and 0 units down, meaning there is no movement. The provided answer choice of 4 units right and 2 units down is incorrect.

Describe the translation from C to A.

Answer explanation

The translation from C to A is 0 units left and 0 units down, meaning there is no movement required. The answer choices suggesting movement are incorrect.