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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 :

GinnyAnsweridn
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].
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