Point A is at #(-9 ,7 )# and point B is at #(2 ,1 )#. 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?

1 Answer
May 12, 2018

#color(blue)("New coordinates of point A due to rotation "(9,-7)#

#color(brown)("Reduction in distance due to rotation of point A by " pi^c#

#color(crimson)(bar (AB) - bar (A'B) = 12.53 - 10.63 = 1.9#

Explanation:

#A (-9,7), B (2,1)," Point A rotated clockwise by p" pi^c#

https://teacher.desmos.com/activitybuilder/custom/566b16af914c731d06ef1953

#A'(x,y) = A'(9,-7)#

#"Distance " = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)#

#bar(AB) = sqrt((-9-2)^2 + (7-1)^2) = 12.53#

#bar(A'B) = sqrt((9-2)^2 + (-7-1)^2) = 10.63#

#color(brown)("Reduction in distance due to rotation of point A by " pi^c#

#color(crimson)(bar (AB) - bar (A'B) = 12.53 - 10.63 = 1.9#