Point A is at #(-3 ,8 )# and point B is at #(-7 ,-5 )#. 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?

1 Answer
Jim G.
Feb 11, 2018

#(8,3),~~3.40#

Explanation:

#"under a clockwise rotation about the origin of "pi/2#

#• " a point "(x,y)to(y,-x)#

#rArrA(-3,8)toA'(8,3)"where A' is the image of A"#

#"to calculate the distance use the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=A(-3,8)" and "(x_2,y_2)=B(-7,-5)#

#AB=sqrt((-7+3)^2+(-5-8)^2)=sqrt(16+169)=sqrt185#

#"let(x_1,y_1)=A'(8,3)" and "(x_2,y_2)=B(-7,-5)#

#A'B=sqrt((-7-8)^2+(-5-3)^2)=sqrt(225+64)=17#

#"change in distance "=17-sqrt185~~3.40#

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