Point A is at $(-3 ,-4 )$ and point B is at $(5 ,8 )$ . 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 · 2018-03-31T16:56:47

$A'(3, 4)$

The distance has decreased from $4sqrt(13) to 2sqrt(5)$

Given: $A(-3, -4), B(5, 8)$ ; rotate $A$ by $pi " radians"=180^@$ clockwise (CW).

distance $AB = sqrt((8- -4)^2 + (5 - -3)^2) = sqrt(12^2 + 8^2)$

$AB= sqrt(208) = sqrt(16*13) = sqrt(16)sqrt(13) = 4sqrt(13)~~14.422$

A CW $pi = 180^@$ transformation is $(x, y) -> (-x, -y)$

New transformation: $" "A' = (3, 4)$

distance $A'B = sqrt((8-4)^2 + (5-3)^2) = sqrt(4^2 + 2^2)$

$A'B = sqrt(20) = sqrt(4)sqrt(5) = 2sqrt(5) ~~4.47$

The distance has decreased from $4sqrt(13) to 2sqrt(5)$

The distance has decreased from $~~14.422 to ~~4.47$ which is a decrease of $~~9.950$

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Point A is at (-3 ,-4 )(-3 ,-4 ) and point B is at (5 ,8 )(5 ,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?