Point A is at #(-2 ,5 )# and point B is at #(-3 ,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 · 2018-07-15T09:49:47

As below.

#A (-2, 5), B (-3, 3), " A rotated " pi " clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((-2+ 3)^2 + (5 - 3)^2) ~~ 2.2361#

#A (-2, 5) to A'(2, -5), " as per rotation rule"#

#bar (A'B) = sqrt((2 + 3)^2 + (-5 - 3)^2) = 9.434#

#"Change in distance "= 9.434 - 2.2361 = 7.198#

#color(blue)(7.198 " is the change in the distance between A & B"# #color(crimson)("due to the rotation of A by " pi " clockwise about the origin"#