Point A is at #(5 ,2 )# and point B is at #(2 ,-4 )#. 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?

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Answer 1 · 2018-02-06T11:46:23

New coordinate of #color(red)(A (-2,5)#

Reduction in distance due to rotation around origin is

#color(green)(bar(AB) - bar(A'B) = sqrt45 - sqrt17 ~~ 2.59)# units

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Point A (5,2), Point B (2, -4)

Point A rotated by #(3pi)/2# about the origin clockwise.

Point A moves from Quadrant I to Quadrant II

#A ((5),(2)) -> A'( (-2),( 5))#

Distance formula #d = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)#,

#bar(AB) = sqrt((5-2)^2 + (2-(-4))^2) = sqrt45#

#bar(A'B) = sqrt((-2-2)^2 + (5-(-4))^2) = sqrt17#

Reduction in distance due to rotation around origin is

#color(green)(bar(AB) - bar(A'B) = sqrt45 - sqrt17 ~~ 2.59)# units