Point A is at $(9 ,3 )$ and point B is at $(1 ,-3 )$ . Point A is rotated $pi/2$ 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 · 2018-03-29T02:42:33

$color(green)("Change in distance " = 2.65 " units")$

$A (9, 3), B (1, -3), "Point A rotated about origin clockwise by " (pi/2)$

To find change in distance between A & B due to this rotation.

Using distance formula,

$vec(AB) = sqrt ((9-1)^2 + (3 + 3)^2) = 10$

![http://www.scielo.org.za/ scielo.php

$A((9),(3)) -> A'((-3),(9))$

$vec(A'B) = sqrt((-3-1)^2 + (9+3)^2) = 12.65$

$"Change in distance =" = vec(A'B) - vec(AB) = 12.65 - 10 = 2.65$

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