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klio [65]
2 years ago
9

What is the location of the image of P(−8, 1) after a counterclockwise rotation of 90° about (−2, 6) ?

Mathematics
1 answer:
storchak [24]2 years ago
5 0

Answer:

(3, 0)

Step-by-step explanation:

Given:

  • Image:  P = (-8, 1)
  • Center of rotation:  (-2, 6)

<u>Rotation rule</u> for -90°:  (x, y) → (y, -x)

As the <u>center of rotation</u> is not the <u>origin</u>, we cannot simply apply the above rule.

To <u>rotate</u> an image around a <u>point other than the origin</u>:

1.  Subtract each point of the image from the point of rotation:

⇒ Point of rotation - point of image

⇒ (-2, 6) - P = (-2, 6) - (-8, 1)

                    = (6, 5)

2. Rotate this about the origin by applying the rotation rule:

⇒ (x, y) → (y, -x)

⇒ (6, 5) → (5, -6)

Add the point of rotation to each rotated point of the image:

⇒ (5, -6) + (-2, 6) = (3, 0)

Therefore, the location of the image of P (-8, 1) after a counterclockwise rotation of 90° about (-2, 6) is (3, 0).

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