Translations & Reflections

When you reflect a shape, you ______ over an axis or line.

• Flip

• Rotate

• Slide

• Expand

Answer explanation

When you reflect a shape, you 'flip' it over an axis or line, creating a mirror image. This distinguishes reflection from other transformations like rotation, sliding, or expanding.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Going from (x,y) to (-x,y) results in reflecting across _______.

• The x-axis

• The y-axis

• The line y=x

• The origin

Answer explanation

Going from (x,y) to (-x,y) changes the x-coordinate's sign while keeping the y-coordinate the same. This transformation reflects the point across the y-axis, making 'The y-axis' the correct answer.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What type of transformation is shown by this rule? (x, y)----> (x + 3, y)

• Rotation

• Reflection

• Translation

• Dilation

Answer explanation

The rule (x, y) --> (x + 3, y) indicates a shift of the point 3 units to the right along the x-axis, which is characteristic of a translation. Therefore, the correct answer is Translation.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Identify the transformation from ABC to A'B'C'.

• Translation 2 units down

• Translation 4 units down

• Reflection across the y-axis

• Reflection across the x-axis

Answer explanation

The transformation from ABC to A'B'C' is a reflection across the x-axis. This means that each point's y-coordinate is negated, resulting in the new coordinates of A', B', and C' being directly opposite their original positions on the y-axis.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Where would A' be if you translated A 3 units to the right and 4 units down?

• (-4, 4)

• (-1, 0)

• (0, -1)

Answer explanation

To find A' after translating A 3 units right and 4 units down, subtract 3 from the x-coordinate and 4 from the y-coordinate. If A is at (2, 4), A' would be (2-3, 4-4) = (-1, 0). Thus, the correct answer is (-1, 0).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Determine how to translate triangle A'B'C' to triangle ABC.

• (x+2, y-5)

• (x+2, y-9)

• (x-2, y-9)

Answer explanation

To translate triangle A'B'C' to triangle ABC, we need to move it 2 units to the right and 9 units down. The correct translation is (x+2, y-9), which matches the coordinates needed to align the triangles.

Tags

CCSS.HSG.CO.A.2

A triangle has vertices at (1, 2), (3, 4), and (5, 6). If the triangle is translated 2 units left and 3 units down, what are the new coordinates of the vertices?

• (-1, -1), (1, 1), (3, 3)

• (3, 5), (5, 7), (7, 9)

• (0, 0), (2, 2), (4, 4)

• (1, 2), (3, 4), (5, 6)

Answer explanation

To translate the triangle, subtract 2 from the x-coordinates and 3 from the y-coordinates of each vertex. The new coordinates are: (1-2, 2-3) = (-1, -1), (3-2, 4-3) = (1, 1), (5-2, 6-3) = (3, 3). Thus, the correct choice is (-1, -1), (1, 1), (3, 3).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Identify the transformation from ABC to A'B'C'.

• (x+8, y+4)

• (x-8, y-4)

• (x+4, y+8)

• (x-4, y-8)

Answer explanation

The transformation from ABC to A'B'C' involves shifting the coordinates. The correct choice (x+8, y+4) indicates a movement 8 units to the right and 4 units up, matching the change in position from ABC to A'B'C'.

Tags

CCSS.HSG.CO.A.2

Write a rule for the translation.

•  (x -1, y  + 2)

•  (x -2, y  + 1)

•  (x +2, y  - 1)

• (x +1, y  -  2)

Answer explanation

The translation rule (x +2, y - 1) indicates moving the point 2 units to the right and 1 unit down. This matches the correct answer, as it specifies the exact changes in the x and y coordinates.

Tags

CCSS.HSG.CO.A.2

Is the picture being reflected in the y-axis or x-axis?

• y-axis

• x-axis

Answer explanation

The picture is reflected in the y-axis, meaning it is mirrored across the vertical line. This results in the left side of the image appearing on the right and vice versa, confirming the correct answer is y-axis.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5