Point A is at (1 ,3 ) and point B is at (2 ,-1 ). 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
Jun 30, 2018

color(purple)(3.12 " 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 (1,3), B (2,-1), " A rotated "pi/2 " clockwise about origin"

#"To find change in distance of AB"

Using distance formula between two points,

bar(AB) = sqrt ((1-2)^2 + (3+1)^2) ~~ 4.12

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

A (1,3) to A'(3,-1), " as per rotation rule"

bar (A'B) = sqrt((3-2)^2 + (-1+1)^2) ~~ 1

"Change in distance "= 4.12 - 1 = 3.12

color(purple)(3.12 " is the change in the distance between A & B" color(purple)("due to the rotation of A by " (pi)/2 " clockwise about the origin"