Point A is at #(-3 ,-4 )# and point B is at #(-5 ,-8 )#. 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 · 2018-06-30T02:45:48

#color(cyan)(5.83 " is the change in the distance between A & B"# #color(cyan)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"#

#A (-3, -4), B (-5, -8), " A rotated "(3pi)/2 " clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((-3 + 5)^2 + (-4 + 8)^2) ~~ 4.47#

#A (-3, -4) to A'(4, -3), " as per rotation rule"#

#bar (A'B) = sqrt((4 + 5)^2 + (-3 + 8)^2) ~~ 10.3#

#"Change in distance "= 10.3 - 4.47 = 5.83#

#color(cyan)(5.83 " is the change in the distance between A & B"# #color(cyan)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"#