Point A is at $(1 ,6 )$ 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 · 2018-02-06T12:13:23

New coordinates of $color(brown)(A (-6, -1)$

Reduction is distance due to rotation is $color(green)( ~~ 1.52$ units

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A (1,6), B (5, -8)

From I to III quadrant

$A ((1),(6))-> A' ((-6), (-1))$

$bar(AB) = sqrt((1-5)^2 + (6-(-8))^2 = sqrt212$

$bar(A'B) = sqrt((-6-5)^2 + (-1+8)^2) = sqrt170$

Reduction is distance due to rotation is

$color(green)(sqrt212 - sqrt170 ~~ 1.52$ units

Point A is at (1 ,6 )(1 ,6 ) 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?