Point A is at #(6 ,4 )# 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 · 2018-03-29T07:52:50

#color(brown)("Decrease in distance due to rotation " #

#color(green)(= vec (AB) - vec(A'B) = 8.54 - 2.24 = 6.3 " units"#

#A (6,4), B (-2, 7)#

#"A rotated about origin by " (3pi)/2 " clockwise"#

#vec (AB) ' sqrt((6+2)^2 + (4-7)^2) = 8.54 " units"#

#A (6,4) -> A'(-4, 6), " rotated clockwise by " (3pi)/2 " about origin"#

#vec (A'B) = sqrt((-4+2)^2 + (6-7)^2) = 2.24 " units"#

#color(brown)("Decrease in distance due to rotation " #

#color(green)(= vec (AB) - vec(A'B) = 8.54 - 2.24 = 6.3 " units"#