Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

What is the coordinate for the image of point [tex]\( H(2, -6) \)[/tex] under a [tex]\( 90^{\circ} \)[/tex] clockwise rotation about the origin?

A. [tex]\( H^{\prime}(-6, -2) \)[/tex]
B. [tex]\( H^{\prime}(6, -2) \)[/tex]
C. [tex]\( H^{\prime}(-6, 2) \)[/tex]
D. [tex]\( H^{\prime}(6, 2) \)[/tex]

Sagot :

GinnyAnswer
To find the coordinates of the image of point [tex]\( H(2, -6) \)[/tex] under a [tex]\( 90^\circ \)[/tex] clockwise rotation about the origin, we follow these steps:

1. Understand the Rotation Rule:
When a point [tex]\((x, y)\)[/tex] is rotated [tex]\(90^\circ\)[/tex] clockwise about the origin, its new coordinates [tex]\((x', y')\)[/tex] are given by:
[tex]\[ (x', y') = (y, -x) \][/tex]

2. Apply the Rotation:
Given the original point [tex]\( H(2, -6) \)[/tex]:
- [tex]\( x = 2 \)[/tex]
- [tex]\( y = -6 \)[/tex]

Substitute these values into the rotation rule:
[tex]\[ x' = y = -6 \][/tex]
[tex]\[ y' = -x = -2 \][/tex]

3. Determine the New Coordinates:
After applying the rotation, the new coordinates of [tex]\( H \)[/tex] are:
[tex]\[ H'(-6, -2) \][/tex]

So, the image of point [tex]\( H(2, -6) \)[/tex] under a [tex]\( 90^\circ \)[/tex] clockwise rotation about the origin is:
[tex]\[ H'(-6, -2) \][/tex]

Therefore, the correct answer is [tex]\( H'(-6, -2) \)[/tex].
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.