Point A is at $(-8 ,2 )$ and point B is at $(2 ,-1 )$ . Point A is rotated $pi/2$ 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?

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Answer 1 · 2018-02-06T12:24:33

New coordinates of $A' color(blue)(((2), (8))$

Reduction in distance due rotation of A by $pi/2$ clockwise is

$color(green)(= sqrt109 - 9 ~~ 1.44$

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A (-8, 2), B (2, -1)

Rotation of A $(pi/2)$ clockwise about origin

A moves from II to I quadrant.

New coordinates of A

$A ((-8),(2)) -> A' color(blue)(((2), (8))$

$bar(AB) = sqrt((-8-2)^2 + (2-(-1))^2) = color(brown)(sqrt109$

$bar(A'B) = sqrt((2-2)^2 + (8-(-1))^2) = color(brown)(9$

Reduction in distance due rotation of A by $pi/2$ clockwise is

$color(green)(= sqrt109 - 9 ~~ 1.44$

Point A is at (-8 ,2 )(-8 ,2 ) and point B is at (2 ,-1 )(2 ,-1 ). Point A is rotated pi/2 pi/2 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?