Question

Please Help

Rotate MAP 90° degrees clockwise about point P. List the new ordered pairs.

Pre Image MAP:
M: (-3, 4)
A: (-7, 7)
P: (-7, -1)​

Answer 1

M' (-2 , -5), A'(1 , -1), P'(-7 , -1)

Explanation:

Rotation clockwise 90° = rotation CCW 270°

Formula for rotation CCW 270° around a point (x',y') for original (x,y)

x'' = (x-x') cos 270° - (y-y') sin 270° + x'

y'' = (x-x') sin 270° + (y-y') cos 270° + y'

cos 270° = 0 and sin 270° = -1

x'' = - (y-y') sin 270° + x' = (y-y') + x'

y'' = (x-x') sin 270° + y' = (x'-x) + y'

M': x = (4 - -1) + (-7) = -2

y = (-7 - -3) + (-1) = -5

A': x = (7 - -1) + (-7) = 1

y = (-7 - -7) + (-1) = -1

check

P': x = (-1 - -1) + (-7) = -7

y = (-7 - -7) + (-1) = -1

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Another way of thinking is to suppose P is (0,0) and locate other points' coordinate relative to P. Such as M(4,5), A(0,8)..

when it rotate CW 90° (x,y) -> (y , -x) will becomes (5 , -4) and (8 , 0). while (5 , -4) relative to p(-7 , -1) is (-7+5 , -1-4) i.e. ( -2 , -5) at original plane and (1 , -1) for point A'

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