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When describing a rotation, which of the following directions is applicable for a rotation?(1 point)

Responses

down
down

counterclockwise
counterclockwise

up
up

right

9 answers

When describing a rotation, the applicable direction is counterclockwise.

Describe the transformation in the diagram.

(1 point)
Responses

180° counterclockwise rotation about the origin
180 degrees counterclockwise rotation about the origin

90° clockwise rotation about the origin
90 degrees clockwise rotation about the origin

270° counterclockwise rotation about the origin
270 degrees counterclockwise rotation about the origin

90° counterclockwise rotation about the origin

To accurately describe the transformation, we would need to see the diagram in question. However, if you can provide details on the position of the points before and after the transformation, I can help you determine which description fits best.

If you are looking for general guidance:

  • A 180° counterclockwise rotation about the origin will take a point (x, y) to (-x, -y).
  • A 90° clockwise rotation about the origin will take a point (x, y) to (y, -x).
  • A 270° counterclockwise rotation about the origin is equivalent to a 90° clockwise rotation; it will transform (x, y) to (-y, x).
  • A 90° counterclockwise rotation about the origin will take a point (x, y) to (-y, x).

If you provide specific coordinates or a description of the transformation, I can assist further!

A segment has endpoints X(−10,0) and Y(−2,6) . Consider its image after a 180° (counterclockwise) rotation about the origin. Select the coordinates of Y′ .(1 point)
Responses

Y′(2,−6)
upper Y prime left parenthesis 2 comma negative 6 right parenthesis

Y′(6,−2)
upper Y prime left parenthesis 6 comma negative 2 right parenthesis

Y′(−2,−6)
upper Y prime left parenthesis negative 2 comma negative 6 right parenthesis

Y′(−6,2)

To determine the coordinates of \( Y' \) after a 180° counterclockwise rotation about the origin, you can use the rule for 180° rotation, which transforms a point \((x, y)\) to \((-x, -y)\).

The coordinates of point \( Y \) are given as \( (-2, 6) \).

Applying the transformation: \[ Y' = (-(-2), -(6)) = (2, -6) \]

So, the coordinates of \( Y' \) are \( (2, -6) \).

The correct response is:

Y′(2,−6).

Imagine a 90° (counterclockwise) rotation about the origin of the figure in the image. Select the coordinate of D′ .

(1 point)
Responses

(8,4)
left parenthesis 8 comma 4 right parenthesis

(−8,4)
left parenthesis negative 8 comma 4 right parenthesis

(4,−8)
left parenthesis 4 comma negative 8 right parenthesis

(8,−4)

To determine the coordinates of point \( D' \) after a 90° counterclockwise rotation about the origin, you can use the rule for this type of rotation. The transformation takes a point \((x, y)\) to \((-y, x)\).

Since the coordinates of point \( D \) are not provided in your question, I'll demonstrate how to calculate the new coordinates assuming the original coordinates of point \( D \) are \( (x, y) \):

  1. Replace \( x \) with \(-y\).
  2. Replace \( y \) with \( x\).

Now, let's check each of the options provided to see which could be a valid result:

  • For the option \( (8, 4) \):

    • If \( D = (4, 8) \): The transformed coordinates would be \((-8, 4)\).

  • For the option \( (-8, 4) \):

    • If \( D = (4, -8) \): The transformed coordinates would be \( (8, -4)\).

  • For the option \( (4, -8) \):

    • If \( D = (-8, 4) \): The transformed coordinates would not match \( D' \).

  • For the option \( (8, -4) \):

    • If \( D = (-4, 8) \): The transformed coordinates would be \( (-8, 4)\).

Without the original coordinate \( D \), we cannot definitively choose the correct answer, but you can use the transformation rule on the original coordinates of point \( D \) to find \( D' \).

If you can provide the original coordinates of point \( D \), I can help to identify which of the options is correct!

Use the image to answer the question.

A quadrilateral is plotted a coordinate plane with both the axes ranging from negative 6 to 6.

Imagine a counterclockwise rotation of 270° about the origin of the figure. Choose the coordinate of A′ .

(1 point)
Responses

(−1,−2)
left parenthesis negative 1 comma negative 2 right parenthesis

(1,2)
left parenthesis 1 comma 2 right parenthesis

(2,−1)
left parenthesis 2 comma negative 1 right parenthesis

(1,1)

To determine the coordinates of \( A' \) after a 270° counterclockwise rotation about the origin, you can use the transformation rule for this type of rotation:

A 270° counterclockwise rotation is equivalent to a 90° clockwise rotation. The transformation takes a point \((x, y)\) to \((y, -x)\).

Since the original coordinates of point \( A \) are not provided in your question, I'll show how to apply the transformation using an example with original coordinates \( (x, y) \):

  1. Take \( A = (x, y) \).
  2. Transform to \( A' = (y, -x) \).

Now let’s analyze each option provided without knowing the original coordinates of \( A \):

  • For the option \( (-1, -2) \):

    • Original could be \( (-2, -1) \) → This does not work since \( (-1, -2) \) does not match the transformation.

  • For the option \( (1, 2) \):

    • Original could be \( (2, -1) \) → This does not work since \( (1, 2) \) does not match the transformation.

  • For the option \( (2, -1) \):

    • Original could be \( (-1, 2) \) → The transformation would give \( (2, 1) \), also does not work.

  • For the option \( (1, 1) \):

    • Original could be \( (1, -1) \) → The transformation would give \( (1, -1) \), correct.

Without the specific coordinates of point \( A \), I cannot definitively select the accurate result. However, please apply the rule of \( (y, -x) \) on the original coordinates of \( A \) to determine \( A' \).

If you know the coordinates of \( A \), I can give you a precise answer!