Point A is at $(5 ,7 )$ 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?

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Answer 1 · 2017-05-16T18:16:45

The new coordinates are $=(7,-5)$ and the distance has changed by $=7.14$

The matrix of a rotation clockwise by $1/2pi$ about the origin is

$=((cos(-1/2pi),-sin(-1/2pi)),(sin(-1/2pi),cos(-1/2pi)))=((0,1),(-1,0))$

Therefore, the trasformation of point $A$ is

$A'=((0,1),(-1,0))((5),(7))=((7),(-5))$

Distance $AB$ is

$=sqrt((-2-5)^2+(6-7)^2)$

$=sqrt(49+1)$

$=sqrt50$

Distance $A'B$ is

$=sqrt((-2-7)^2+(6+5)^2)$

$=sqrt(81+121)$

$=sqrt202$

The distance has changed by

$=sqrt202-sqrt50$

$=7.14$

Point A is at (5 ,7 )(5 ,7 ) and point B is at (-2 ,6 )(-2 ,6 ). 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?