Question

Rotations Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. Imagine a 90° (counterclockwise) rotation about the origin of the figure in the image. Select the coordinate of D′ . (1 point) Responses (4,−8) left parenthesis 4 comma negative 8 right parenthesis (−8,4) left parenthesis negative 8 comma 4 right parenthesis (8,−4) left parenthesis 8 comma negative 4 right parenthesis (8,4)

Answer 1

To find the coordinates of point D' after a 90° counterclockwise rotation about the origin, you can apply the following transformation to the coordinates of point D (x, y):

• The formula for a 90° counterclockwise rotation is:
  • \( D'(x', y') = (-y, x) \)

If you have the original coordinates of point D, you can substitute them into this formula.

For example:

• If the original point D is (4, -8), applying the transformation gives:
  • \( x' = -(-8) = 8 \)
  • \( y' = 4 \)

Thus, the new coordinates after the rotation would be (8, 4).

Please specify the original coordinates of point D to provide an accurate answer. If D is indeed (4, -8), then the correct response is (8, 4).

Answer 2

se the image to answer the question. 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 (1,1) left parenthesis 1 comma 1 right parenthesis (2,−1)

Answer 3

To find the coordinates of point A' after a 270° counterclockwise rotation about the origin, you can use the following transformation:

• The formula for a 270° counterclockwise rotation is equivalent to a 90° clockwise rotation, which can be expressed as:
  • \( A'(x', y') = (y, -x) \)

If you have the original coordinates of point A (let's say they are (x, y)), substitute those values into the formula.

For example:

• If the original point A is (x, y):
  • \( x' = y \)
  • \( y' = -x \)

In order to provide an accurate response, please provide the original coordinates of point A.

However, if we assume the initial coordinates of point A are (1, 2), after a 270° counterclockwise rotation the coordinates would be:

• \( x' = 2 \)
• \( y' = -1 \)

Thus, the new coordinates A' would be (2, -1).

Based on this calculation, if the original coordinates of point A were indeed (1, 2), then the correct response would be (2, -1).