Point A is at (-7 ,-1 )(−7,−1) and point B is at (2 ,-4 )(2,−4). Point A is rotated pi π 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?

1 Answer
sankarankalyanam
Jun 30, 2018

color(indigo)(2.42" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"2.42 is the change in the distance between A & B due to the rotation of A by 3π2 clockwise about the origin

Explanation:

A (-7, -1), B (2, -4), " A rotated " pi " clockwise about origin"A(−7,−1),B(2,−4), A rotated π clockwise about origin

#"To find change in distance of AB"

Using distance formula between two points,

bar(AB) = sqrt ((-7 -2)^2 + (-1 +4)^2) ~~ 9.49¯¯¯¯¯¯AB=√(−7−2)2+(−1+4)2≈9.49

![https://www.onlinemath4all.com/http://rotation-transformation.html](https://useruploads.socratic.org/VA3bKvvS3K8G1tSlViNi_rotation%20rules.jpg)

A (-7, -1) to A'(7,1), " as per rotation rule"

bar (A'B) = sqrt((7-2)^2 + (1+4)^2) ~~ 7.07

"Change in distance "= 9.49 - 7.07 = 2.42

color(indigo)(2.42" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"

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