Point A is at $(-9 ,-1 )$ and point B is at $(3 ,-4 )$ . 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 · 2018-02-22T08:54:48

Decrease in distance due to clockwise rotation by $pi$ is

$color(blue)(d = 4.5591$

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Given $A (-9,-1)$ , $B(3,-4)$

Rotated about origin by $pi$ , clockwise.

$vec(AB) = sqrt((-9-3)^2 + (-1+4)^2) = 12.3693$

$A((-9),(-1))-> A’((9),(1))$

$vec(A’B) = sqrt((9-3)^2 + (1+4)^2) = 7.8102$

Decrease in distance due to clockwise rotation by $pi$ is

$d = 12.3693 - 7.8102 = 4.5591$

Point A is at (-9 ,-1 )(-9 ,-1 ) and point B is at (3 ,-4 )(3 ,-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?