Point A is at $(9 ,3 )$ and point B is at $(1 ,-6 )$ . 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 · 2017-06-28T07:18:12

The new coordinates are $=(3,-9)$ and the distance has changed by $=8.4$

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

$((0,1),(-1,0))$

Therefore, the transformation of point $A$ is

$A'= ((0,1),(-1,0)) ((9),(3))=((3),(-9))$

The distance $AB$ is

$=sqrt((1-(9))^2+(-6-3)^2)$

$=sqrt(64+81)$

$=sqrt145$

The distance $A'B$ is

$=sqrt((1-(3))^2+(-6-(-9))^2)$

$=sqrt(4+9)$

$=sqrt13$

The distance has changed by

$=sqrt145-sqrt13$

$=8.4$

Point A is at (9 ,3 )(9 ,3 ) and point B is at (1 ,-6 )(1 ,-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?