Point A is at (1 ,3 ) and point B is at (2 ,6 ). 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
Mar 29, 2018

color(maroon)("Increase in distance due to the rotation is "

color(crimson)(vec(A'B) - vec(AB) = 7.07 - 3.16 = 3.9 " units"

Explanation:

Given ": A (1,3), B (2,6), "Point A rotated by " pi/2 " clockwise about the origin"

vec (AB) = sqrt((1-2)^2 + (3-6)^2) = 3.16 " units"

![https://www.onlinemath4all.com/http://rotation-transformation.html](https://useruploads.socratic.org/eQh53A0SfiedyGDRIswA_rotation%20rules.jpg)
A (1,3) -> A' (3, -1)

vec(A'B) = sqrt((3-2)^2 + (-1-6)^2) = 7.07 " units"

color(maroon)("Increase in distance due to the rotation is "

color(crimson)(vec(A'B) - vec(AB) = 7.07 - 3.16 = 3.9 " units"

Related questions
See all questions in Rotations
Impact of this question
1852 views around the world
You can reuse this answer
Creative Commons License