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Point A is at #(2 ,5 )# and point B is at #(1 ,-6 )#. 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?

Answer 1

Jayden Jackson

#vec(AB)# has reduced by #color(brown)(7.8831)# due to rotation of #pi# clockwise about the origin.

#A((2),(5)) -> A’((-2),(-5))#. I to III quadrant.

# vec (AB) = sqrt ((2-1)^2 + (5+6)^2) = 11.0454#

#vec (A’B) = sqrt ((-2-1)^2 + (-5+6)^2) = 3.1623#

#vec(AB) - vec(A’B) = 11.0454 - 3.1623 = 7.8831#

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Answer 2

Ella Armstrong

The new coordinates of point A after rotating (\pi) clockwise about the origin are (-2, -5). The distance between points A and B remains unchanged after the rotation, as rotations about the origin preserve distances. Therefore, the distance between points A and B remains the same as it was originally.

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