Point A is at #(-3 ,-4 )# and point B is at #(1 ,8 )#. 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?

1 Answer
sankarankalyanam
Jun 30, 2018

#color(orange)(8.18 " is the reduction in the distance between A & B"# #color(orange)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"#

Explanation:

#A (-3, -4), B (1, 8), " A rotated "pi " clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((-3 -1)^2 + (-4 - 8)^2) ~~ 12.65#

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

#A (-3, -4) to A'(3, 4), " as per rotation rule"#

#bar (A'B) = sqrt((3-1)^2 + (4-8)^2) ~~ 4.47#

#"Change in distance "= 12.65 - 4.47 = 8.18#

#color(orange)(8.18 " is the reduction in the distance between A & B"# #color(orange)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"#

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