Point A is at $(9 ,5 )$ and point B is at $(2 ,4 )$ . 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 · 2017-07-06T09:28:32

The new coordinates are $(-9,-5)$ and the distance has changed by $=7.14$

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

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

Therefore, the transformation of point $A$ is

$A'=((-1,0),(0,-1))((9),(5))=((-9),(-5))$

The distance $AB$ is

$AB=sqrt((2-9)^2+(4-5)^2)$

$=sqrt(49+1)$

$=sqrt50$

The distance $A'B$ is

$A'B=sqrt((2-(-9))^2+(4-(-5))^2)$

$=sqrt(121+81)$

$=sqrt202$

The distance has changed by

$=sqrt202-sqrt50$

$=7.14$

Point A is at (9 ,5 )(9 ,5 ) and point B is at (2 ,4 )(2 ,4 ). 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?