Point A is at (5 ,-8 ) and point B is at (-3 ,3 ). 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
Somebody N.
May 27, 2018

See below.

Explanation:

A rotation of pi/2 clockwise maps:

(x,y)->(-y,x)

Points: A=(5,-8), (-3,3)

:.

A'=(5,-8)->(-y,x)=(8,5)

B'=(-3,3)->(-y,x)=(-3,-3)

Where A' and B' are the images of A and B respectively.

Using the distance formula to find the distance between A and B and A' and B'

A and B

d=sqrt((-3-5)^2+(3-(-8)))=sqrt(185)

A' and B'

d=sqrt((-3-8)^2+(-3,-5)^2)=sqrt(185)

We didn't need to even calculate this. A rotation doesn't change the relative distance between points. The question is very ambiguous when it asks for distance between A and B. I have assumed it meant between A' and B'.

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