Point A is at #(5 ,7 )# and point B is at #(-6 ,-3 )#. 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 · 2018-04-08T05:20:25

#color(brown)("There is no change in the distance between A & B due to the rotation of " (3pi)/2 " clockwise about the origin"#

#A (5,7), B (-6, -3), " A rotated (3pi)/2 clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((5 + 6)^2 + (7 + 3)^2) = 14.87#

#A (5, 7) to A'(-7,5), " as per rotation rule"#

#B(-6, -3) to B'(3, -6), " as per rotation rule"#

#bar (A'B') = sqrt((-7-3)^2 + (5 + 6)^2) = 14.87#

#color(brown)("There is no change in the distance between A & B due to the rotation of " (3pi)/2 " clockwise about the origin"#