Point A is at (5 ,3 ) and point B is at (-3 ,2 ). Point A is rotated pi/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

color(purple)(1.16 " is the change in the distance between A & B" color(orange)("due to the rotation of A by " (pi)/2 " clockwise about the origin"

Explanation:

A (5,3), B (-3, 2), " A rotated "pi/2 " clockwise about origin"

#"To find change in distance of AB"

Using distance formula between two points,

bar(AB) = sqrt ((5+3)^2 + (3-2)^2) ~~ 8.06

![https://www.onlinemath4all.com/http://rotation-transformation.html](https://useruploads.socratic.org/VA3bKvvS3K8G1tSlViNi_rotation%20rules.jpg)

A (5,3) to A'(3,-5), " as per rotation rule"

bar (A'B) = sqrt((3+3)^2 + (-5-2)^2) ~~ 9.22

"Change in distance "= 9.22 - 8.06 = 1.16

color(purple)(1.16 " is the change in the distance between A & B" color(orange)("due to the rotation of A by " (pi)/2 " clockwise about the origin"

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