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Point A is at #(1 ,-9 )# and point B is at #(-2 ,8 )#. 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?

Answer 1

Sadie Allen

The new point A will be at #(9, 1)#
Difference in distance #=sqrt(298)-sqrt(170)=13.0384" "#units

The old distance between #A# and #B# is

distance #d=sqrt((x_a-x_b)^2+(y_a-y_b)^2)#

#d=sqrt((1--2)^2+(-9-8)^2)#

#d=sqrt((3)^2+(-17)^2)#

#d=sqrt(9+289)#

#d=sqrt(298)#

The new distance between #A# and #B# is

distance #d=sqrt((x_a-x_b)^2+(y_a-y_b)^2)#

#d=sqrt((9--2)^2+(1-8)^2)#

#d=sqrt((11)^2+(-7)^2)#

#d=sqrt(121+49)#

#d=sqrt(170)#

Difference in distance #=sqrt(298)-sqrt(170)=13.0384" "#units

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Answer 2

James Atkins

The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (-9, -1). The distance between the original point A and point B is sqrt(170). After the rotation, the distance between the new point A and point B is also sqrt(170). Therefore, the distance between points A and B has not changed after the rotation.

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