Point A is at (-6 ,1 )(−6,1) and point B is at (2 ,8 )(2,8). Point A is rotated (3pi)/2 3π2 clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

1 Answer
sankarankalyanam
Jul 31, 2018

#color(green)("Change in dist. due to the rotation" = sqrt113 - sqrt65 ~~ 1.3185

Explanation:

![https://www.onlinemath4all.com/http://algebraic-representations-of-rotations.html](https://useruploads.socratic.org/VDbQTQqHTk2bbFn0N4vu_quadrant%20signs.GIF)

A (-6, 1), B (2, 8), " rotated about origin by " (3pi)/2 " clockwise"A(−6,1),B(2,8), rotated about origin by 3π2 clockwise

A (-6, 1) to A' (-1, -6)

B ( 2, 8) to B' (-8, 2)

"Distance " bar(AB) = sqrt ((-6 - 2)^2 + (1 - 2)^2) = sqrt 65

"Distance " bar(A'B') = sqrt ((-1 - -8)^2 + (-6 - 2)^2) = sqrt 113

color(green)("Change in dist. due to the rotation" = sqrt113 - sqrt65 ~~ 1.3185

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