Question

Find the image of (-1,3) obtained by translating 2 units down, followed by a rotation of 270 degrees counterclockwise about the origin

Answer 1

[1, 1]

Explanation:

Translation → [-1, 3] moves down to [-1, 1]

Now, a 90°-clockwise rotation is the exact same as a 270°-counterclockwise rotation, and according to the 270°-counterclockwise rotation [90°-clockwise rotation] rule, you take the y-coordinate, bring it over to your new x-coordinate, and take the OPPOSITE of the x-coordinate and set it as your new y-coordinate:

Extended Rotation Rules

• 270°-clockwise rotation [90°-counterclockwise rotation] >> (x, y) → (-y, x)
• 270°-counterclockwise rotation [90°-clockwise rotation] >> (x, y) → (y, -x)
• 180°-rotation >> (x, y) → (-x, -y)

Then, you perform your rotation:

270°-counterclockwise rotation [90°-clockwise rotation] → [-1, 1] moves to [1, 1]

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