Answered

IDNLearn.com provides a comprehensive platform for finding accurate answers. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.

Tanya's rotation maps point [tex]\( K(24,-15) \)[/tex] to [tex]\( K^{\prime}(-15,-24) \)[/tex]. Which describes the rotation?

A. [tex]\( 90^{\circ} \)[/tex] clockwise rotation
B. [tex]\( 270^{\circ} \)[/tex] clockwise rotation
C. [tex]\( 180^{\circ} \)[/tex] rotation
D. [tex]\( 90^{\circ} \)[/tex] counterclockwise rotation

Sagot :

GinnyAnsweridn
To determine the type of rotation that maps point [tex]\( K(24, -15) \)[/tex] to [tex]\( K'(-15, -24) \)[/tex], we need to analyze how the coordinates change under various rotations.

1. 90 degrees clockwise rotation:
- This transforms a point [tex]\( (x, y) \)[/tex] to [tex]\( (y, -x) \)[/tex].
- Applying this to [tex]\( K(24, -15) \)[/tex]: [tex]\( (24, -15) \)[/tex] becomes [tex]\( (-15, -24) \)[/tex].

2. 270 degrees clockwise rotation:
- This is equivalent to a 90 degrees counterclockwise rotation, transforming [tex]\( (x, y) \)[/tex] to [tex]\( (-y, x) \)[/tex].
- Applying this to [tex]\( K(24, -15) \)[/tex]: [tex]\( (24, -15) \)[/tex] becomes [tex]\( (15, 24) \)[/tex].

3. 180 degrees rotation:
- This transforms a point [tex]\( (x, y) \)[/tex] to [tex]\( (-x, -y) \)[/tex].
- Applying this to [tex]\( K(24, -15) \)[/tex]: [tex]\( (24, -15) \)[/tex] becomes [tex]\( (-24, 15) \)[/tex].

4. 90 degrees counterclockwise rotation:
- This transforms a point [tex]\( (x, y) \)[/tex] to [tex]\( (-y, x) \)[/tex].
- Applying this to [tex]\( K(24, -15) \)[/tex]: [tex]\( (24, -15) \)[/tex] becomes [tex]\( (15, 24) \)[/tex].

On examining the transformations, we see that the coordinates transform [tex]\( K(24, -15) \)[/tex] to [tex]\( K'(-15, -24) \)[/tex] correctly through a 90 degrees clockwise rotation. Thus, the correct description of the rotation that maps [tex]\( K \)[/tex] to [tex]\( K' \)[/tex] is:

90 degrees clockwise rotation.
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.