Point A is at #(-5 ,4 )# and point B is at #(-8 ,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?

1 Answer
sankarankalyanam
Apr 6, 2018

#color(indigo)("Increase in distance due to the rotation " = 8.4065#

Explanation:

#A (-5,4), B(-8,7), " rotated " (3pi)/2 " clockwise about the origin"#

#bar(AB) = sqrt((-5+8)^2 + (4-7)^2) = 4.2426#

https://teacher.desmos.com/activitybuilder/custom/566b16af914c731d06ef1953

#A (-5, 4) to A'( -4,-5)#

#bar(A'B) = sqrt((-4 + 8)^2 + (-5 - 7)^2) = 12.6491#

#color(indigo)("Increase in distance " = 12.6491 - 4.2426 = 8.4065#

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