Point A is at $(-2 ,6 )$ and point B is at $(-7 ,-5 )$ . 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 · 2017-07-14T13:59:34

The new coordinates are $=(6,2)$ and the distance has changed by $=2.68$

The rotation of $pi/2$ clockwise about the origin transforms the point $A$ into $A'$

The coordinates of $A'$ are

$((0,1),(-1,0))*((-2),(6))=((6),(2))$

Distance $AB$ is

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

$=sqrt(25+121)$

$=sqrt(146)$

Distance $A'B$ is

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

$=sqrt(169+49)$

$=sqrt(218)$

The distance has changed by

$=sqrt218-sqrt146$

$=2.68$

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