Point A is at #(1 ,6 )# and point B is at #(5 ,-3 )#. 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(purple)(3.14 " is the reduction in the distance between A & B"# #color(orange)("due to the rotation of A by " pi " clockwise about the origin"#

Explanation:

#A (1, 6), B (5, -3), " A rotated "pi " clockwise about origin"#

#"To find change in distance of AB"

Using distance formula between two points,

#bar(AB) = sqrt ((1-5)^2 + (6+3)^2) ~~ 9.85#

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

#A (1, 6) to A'(-1 - 6), " as per rotation rule"#

#bar (A'B) = sqrt((-1-5)^2 + (-6+3)^2) ~~ 6.71#

#"Change in distance "= 9.85 - 6.71 = 3.14#

#color(purple)(3.14 " is the reduction in the distance between A & B"# #color(orange)("due to the rotation of A by " pi " clockwise about the origin"#

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