Point A is at $(6 ,2 )$ 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 · 2017-06-08T13:30:24

Distance has increased by $9.036$

When a point $(x,y)$ is rotated clockwise about the origin, its new coordintes are $(y,-x)$ .

Hence when $A(6,2)$ is rotated clockwise about the origin, the new coordinates are $(2,-6)$

Originally distance between $(6,2)$ and $(3,8)$ was

$sqrt((3-6)^2+(8-2)^2)=sqrt(9+16)=sqrt25=5$

This changes to

$sqrt((3-2)^2+(8-(-6))^2)=sqrt(1+196)=sqrt197=14.036$

Hence, distance has increased by $14.036-5=9.036$

Point A is at (6 ,2 )(6 ,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?