Point A is at #(-9 ,-6 )# and point B is at #(-2 ,-7 )#. 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 · 2018-06-30T02:33:03

#color(brown)(8.23" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"#

#A (-9,-6), B (-2, -7), " A rotated (3pi)/2 clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((-9 +2)^2 + (-6 +7)^2) = 7.07#

#A (-9, -6) to A'(6,-9), " as per rotation rule"#

#bar (A'B) = sqrt((-9-6)^2 + (-6 +9)^2) ~~ 15.3#

#"Change in distance "= 15.3 - 7.07 = 8.23#

#color(brown)(8.23" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"#