Point A is at #(4 ,-5 )# and point B is at #(-6 ,-2 )#. Point A is rotated #(3pi)/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?

Answer 1

Sadie Allen

New coordinates #A’ (-5,-4)#

Change in distance #1.3849#, reduction.

Given #A (4, -5), B (-6,-2). Rotated about origin by #(3pi)/2#

To find A’ and #A’B - AB#

#vec(AB) = sqrt((4+6)^2 + (-5+2)^2) = sqrt109#

Coordinates of A’ (-5,-4)

#vec(A’B) = sqrt((-5-4)^2 + (-4+5)^2) = sqrt 82#

Change in distance #vec(AB) - vec(A’B) = sqrt109 - sqrt82 ~~ 1.3849#

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Answer 2

Wyatt Anderson

The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (5, 4). The distance between points A and B remains unchanged after the rotation. Therefore, the distance between points A and B has not changed.

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Answer from HIX Tutor

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