Point A is at #(-7 ,-1 )# and point B is at #(2 ,-4 )#. 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 · 2018-06-30T02:38:22

#color(indigo)(2.42" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"#

#A (-7, -1), B (2, -4), " A rotated " pi " clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((-7 -2)^2 + (-1 +4)^2) ~~ 9.49#

#A (-7, -1) to A'(7,1), " as per rotation rule"#

#bar (A'B) = sqrt((7-2)^2 + (1+4)^2) ~~ 7.07#

#"Change in distance "= 9.49 - 7.07 = 2.42#

#color(indigo)(2.42" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"#