Point A is at #(-2 ,5 )# and point B is at #(2 ,-3 )#. Point A is rotated #pi # 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 · 2018-03-29T12:20:29

#color(blue)("Decrease in distance due rotation is "#

#color(orange)(vec(AB) - vec(A'B) = 8.94 - 2 = 6.94 " units"#

#A (-2, 5), B (2, -3)#

#vec (AB) = sqrt((-2-2)^2 + (5 + 3)^2) = 8.94 " units"#

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

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

#vec (A'B) = sqrt ((2-2)^2 + (-5 +3)^2) = 2 " units"#

#color(blue)("Decrease in distance due rotation is "#

#color(grey)(vec(AB) - vec(A'B) = 8.94 - 2 = 6.94 " units"#