Point A is at $(-2 ,-4 )$ and point B is at $(-3 ,3 )$ . 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 · 2018-03-20T11:39:16

Increase in distance due to the rotation of point A is

$color(green)(vec(A'B) - vec(AB) = sqrt74 - sqrt50 = 1.53$

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$"Point " A (-2, -4), "Point " B (-3, 3)$

Point A rotated about origin by $(3pi)/2$ clockwise.

To find change in distance between Ab due to rotation of point A.

$A (-2, -4) -> A' (4,-2) , " shifted from III to IV quadrant"$

Using distance formula,

$vec(AB) = sqrt((-2+3)^2 + (-4-3)^2) = sqrt50$

$vec(A'B) = sqrt((4+3)^2 + (-2-3)^2) = sqrt74$

Increase in distance due to the rotation of point A is

$color(green)(vec(A'B) - vec(AB) = sqrt74 - sqrt50 = 1.53$

Point A is at (-2 ,-4 )(-2 ,-4 ) and point B is at (-3 ,3 )(-3 ,3 ). 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?