Point A is at $(3 ,2 )$ and point B is at $(3 ,-8 )$ . 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?

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Answer 1 · 2016-09-10T22:00:12

The new A is $(2,-3)$ and the difference in the distance is approximately $4.9$ .

A $pi/2$ or $90$ degrees clockwise rotation of a point can be written as $(x,y)->(y,-x)$ .

So, $(3,2)$ rotated $pi/2$ clockwise becomes $(2,-3)$ .

The distance between the original point A (3,2) and B (3,-8) can be found using the distance formula.

$sqrt((3-3)^2+(-8-2)^2$ $= sqrt((-10)^2)$ $=sqrt100$ $=10$

The distance between the new point A (2,-3) and B (3,-8) is

$sqrt((3-2)^2+(-8- -3)^2)$ $=sqrt(1^2+(-5)^2)$ $=sqrt(1+25)$ $=sqrt26$ $~=5.1$

The difference between the A and B changes by approximately $10-5.1 = 4.9$

Point A is at (3 ,2 )(3 ,2 ) and point B is at (3 ,-8 )(3 ,-8 ). Point A is rotated pi/2 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?