Point A is at $(-5 ,9 )$ and point B is at $(-1 ,7 )$ . Point A is rotated $(3pi)/2$ 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 · 2018-02-06T10:06:19

New coordinates of A (-9, -5) & the distance changed (increase) = 9.95 units

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A(-5,9), B(-1,7)

With clockwise rotation by $(3pi)/2$ around the origin

Point A moves from III quadrant to IV quadrant.

$(x,y) -> (-y,x)$

$A(-5,9) -> A' (-9, -5)$

Using distance formula,

$vec(AB) = sqrt(-5 - (-1))^2 + (9-7)^2) = sqrt20$

$vec(AB') = sqrt((-9-(-1))^2 + ((-5)-7)^2) = sqrt208$

$A'B - AB = sqrt208 - sqrt20 = 9.95$ units

Point A is at (-5 ,9 )(-5 ,9 ) and point B is at (-1 ,7 )(-1 ,7 ). Point A is rotated (3pi)/2 (3pi)/2 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?