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Point A is at #(-2 ,-8 )# and point B is at #(-5 ,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?

Answer 1

Savannah Aguilar

Increase in distance due to rotation of point A 1.6816

#A (-2, -8), B (-5, 3)#

Point A rotated clockwise about origin by #pi/2#

#A ((-2), (-8)) -> A’ ((8),(2))# from III to I quadrant.

# vec(AB) = sqrt((-2+5)^2 + (-8-3)^2) = sqrt130 = 11.4018#

#vec (A’B) = sqrt ((8+5)^2 + (2-3)^2) = sqrt170 = 13.0834#

Change in distance due to rotation of point A

#d = 13.0834 - 11.4018 = color(purple)(1.6816#

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Answer 2

Carson Arnold

The new coordinates of point A after rotating π/2 radians clockwise about the origin are (8, -2). The distance between points A and B remains unchanged after the rotation.

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