Point A is at #(-1 ,-5 )# and point B is at #(-2 ,4 )#. Point A is rotated #pi/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 · 2018-03-29T08:13:42

#color(red)("Decrease in distance due to the rotation is "#

#color(crimson)(= vec(AB) - vec(A'B) = 9.055 - 4.243 = 4.812 " units"#

#A (-1, -5), B (-2, 4)#

#"Point A rotated " pi/2 " clockwise about the origin"#

#vec(AB) = sqrt((-1+2)^2 + (-5-4)^2) = 9.055 " units"#

#A (-1, -5) rarr A' (-5, 1)#

#vec (A'B) = sqrt((-5 + 2)^2 + (1 - 4)^2) = 4.243 " units"#

#color(red)("Decrease in distance due to the rotation is "#

#color(crimson)(= vec(AB) - vec(A'B) = 9.055 - 4.243 = 4.812 " units"#