Transformations and Congruence (Module 1)

Which reflection does the image show?

• Reflection across the x-axis according to the rule (x, y) → (x, −y)

• Reflection across the y-axis according to the rule (x, y) → (x, −y)

• Reflection across the x-axis according to the rule (x, y) → (−x, y)

• Reflection across the y-axis according to the rule (x, y) → (−x, y)

Answer explanation

The answer is 'Reflection across the y-axis according to the rule (x, y) → (−x, y)'. This rule specifies that for each point (x, y), we create a new point by reflecting it across the y-axis. The x-coordinate changes its sign while the y-coordinate remains the same, thus resulting in the new point (−x, y). Therefore, the image shows a reflection across the y-axis.

Tags

CCSS.MATH.CONTENT.8.G.A.1

CCSS.MATH.CONTENT.8.G.A.2

CCSS.MATH.CONTENT.8.G.A.3

CCSS.MATH.CONTENT.8.G.A.4

• Reflection

• Rotation

• Translation

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

• Reflection

• Rotation

• Translation

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CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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

• left 2, up 9

• right 2, down 9

• left 2, down 9

• left 2, up 5

Answer explanation

The question asks how triangle ABC can be translated to triangle A'B'C'. The correct answer is 'left 2, up 9'. This means we move each point of the triangle 2 units to the left and 9 units up.

Tags

CCSS.HSG.CO.A.2

Triangle A is rotated 270° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Answer explanation

The triangle A, when rotated 270 degrees clockwise about the origin, would land in the position as shown in the image of option D. This is due to the rules of geometry and rotation about a point.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

A slide is also called a _________.

• Translation

• Reflection

• Rotation

• Transformation

Answer explanation

In the context of the given question, a slide refers to a type of motion in geometry, where an object is moved from one position to another without any rotation or reflection. This type of motion is also known as 'Translation'. Hence, 'Translation' is the correct answer.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

The following is a ...

• Translation

• Reflection

• Rotation

• Dilation

Answer explanation

The given question asks about a certain process. The correct answer is 'Reflection'. In contrast to the other options, Reflection implies the flipping of an object across a line. This makes it distinctive from Translation (shifting of the object without changing its features), Rotation (turning the object around a fixed point), and Dilation (changing size of the object without altering its shape or orientation).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Flipping a figures is a ...

• Rotation

• Reflection

• Dilation

• Translation

Answer explanation

The correct answer to the question 'Flipping a figures is a ...' is 'Reflection'. In the context of geometry, flipping a figure refers to creating a mirror image of the figure, which is known as a 'Reflection'. The other options, 'Rotation', 'Dilation', and 'Translation', do not accurately describe the action of flipping a figure.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Reflect the point (2, -4) over the y-axis.

• (-4, 2)

• (-2, 4)

• (-2, -4)

• (2, 4)

Answer explanation

Reflecting a point over the y-axis changes only the x-coordinate, not the y-coordinate. It changes the sign of x-coordinate i.e., 2 becomes -2. The y-coordinate stays the same i.e., -4 remains -4, hence the correct answer is (-2, -4).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What type of transformation is this?

• Reflction

• Translation

• Dilation

• Rotation

Answer explanation

The question asks about a type of transformation. The correct answer is Translation. In geometry, translation refers to moving an object without rotating it, reflecting it or changing its size or shape which aligns with the question.

Tags

CCSS.HSG.CO.A.2