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
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.htmlhttps://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"