Point A is at #(2 ,-1 )# and point B is at #(9 ,-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
Jun 30, 2018

As below

Explanation:

#A (2,-1), B (9, -7), " A rotated "(3pi)/2 " clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((2-9)^2 + (-1 + 7)^2) ~~ 9.22#

https://www.onlinemath4all.com/rotation-transformation.html

#A (2, -1) to A'(1, 2), " as per rotation rule"#

#bar (A'B) = sqrt((1-9)^2 + (2+7)^2) = 12.04#

#"Change in distance "= 12.04 - 9.22 = 2.82#

#color(blue)(2.82 " is the change in the distance between A & B"# #color(crimson)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"#

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