Point A is at #(9 ,3 )# and point B is at #(1 ,-3 )#. 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 · 2018-03-29T02:42:33

#color(green)("Change in distance " = 2.65 " units")#

#A (9, 3), B (1, -3), "Point A rotated about origin clockwise by " (pi/2)#

To find change in distance between A & B due to this rotation.

Using distance formula,

#vec(AB) = sqrt ((9-1)^2 + (3 + 3)^2) = 10#

#A((9),(3)) -> A'((-3),(9))#

#vec(A'B) = sqrt((-3-1)^2 + (9+3)^2) = 12.65#

#"Change in distance =" = vec(A'B) - vec(AB) = 12.65 - 10 = 2.65#