Point A is at (5 ,1 ) and point B is at (2 ,-4 ). 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
Nov 24, 2016

"The new coordinates of A is (-1,5)"

"distance :"sqrt(90)

Explanation:

"draw A(5,1) and B(2,-4)"

enter image source here

(2pi)-(3pi)/2=pi/2

"clockwise "(3pi)/2 " equals counterclockwise "pi/2

"so " A(x,y) " "A'(-y,x)

"The new Position of A is "A'(-1,5)

enter image source here

enter image source here

"distance between B and A' can be calculated using the triangle A'DB"

A'B=sqrt(3^2+9^2)

A'B=sqrt(9+81)

A'B=sqrt(90)