Point A is at $(2 ,-3 )$ and point B is at $(6 ,-6 )$ . 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?

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Answer 1 · 2016-11-25T17:32:53

$(2, -3)-> (-2,3)$ and $(6, -6)->(-6,6)$

No change in the distance.

The general rule is that in case of clockwise rotation by $pi$ (or 180 degrees), $(x,y) -> (-x-y)$

Thus(2,-3 ) would become (-2, 3) and (6, -6) would become (-6,6)

The distance between A nd B = $sqrt((6-2)^2 +(-6+3)^2)=5$

After rotation the distance would be $sqrt((-6+2)^2 +(6-3)^2)=5$

This shows that there would be no change in the distance between the points after rotation.

Point A is at (2 ,-3 )(2 ,-3 ) and point B is at (6 ,-6 )(6 ,-6 ). Point A is rotated pi 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?