Point A is at $(-2 ,5 )$ and point B is at $(-3 ,8 )$ . Point A is rotated $pi$ 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 · 2017-06-07T12:14:56

The new point is $=(2,-5)$ and the distance has changed by $=12.93$

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

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

Therefore, the trasformation of point $A$ into $A'$ is

$A'=((-1,0),(0,-1))((-2),(5))=((2),(-5))$

Distance $AB$ is

$=sqrt((-3-(-2))^2+(8-(5))^2)$

$=sqrt(1+9)$

$=sqrt10$

Distance $A'B$ is

$=sqrt((-3-(2))^2+(8-(-5))^2)$

$=sqrt(25+169)$

$=sqrt194$

The distance has changed by

$=sqrt194-sqrt10$

$=12.93$

Point A is at (-2 ,5 )(-2 ,5 ) and point B is at (-3 ,8 )(-3 ,8 ). Point A is rotated pi pi 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?