Point A is at #(-8 ,5 )# and point B is at #(-3 ,-2 )#. 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 · 2018-03-29T08:00:07

#color(purple)("Increase in distance due to the rotation "#

#color(crimson)(= vec(A'B) - vec(AB) = 12.8 - 8.6 = 4.2 " units"#

#A (-8,5), B(-3, -2)#

#"Point A rotated " (pi/2) " clockwise about the origin"#

To find change in distance #vec(AB)# due to the rotation.

#vec(AB) = sqrt((-8+3)^2 + (5+2)^2) = 8.6 " units"#

#A (-8, 5) -> A'(5, 8)#

#vec (A'B) = sqrt((5+3)^2 + (8+2)^2) = 12.8 " units"#

#color(purple)("Increase in distance due to the rotation "#

#color(crimson)(= vec(A'B) - vec(AB) = 12.8 - 8.6 = 4.2 " units"#