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Point A is at #(-1 ,-3 )# and point B is at #(-5 ,4 )#. 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?

Answer 1

Autumn Armstrong

#(-3,1),~~4.457#

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

#• " a point "(x,y)to(y,-x)#

#rArrA(-1,-3)toA'(-3,1),"A' is the image of A"#

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))#

#"let "(x_1,y_1)=(-1,-3)" and "(x_2,y_2)=(-5,4)#

#AB=sqrt((-5+1)^2+(4+3)^2)=sqrt(16+49)=sqrt65#

#"let "(x_1,y_1)=(-3,1)" and "(x_2,y_2)=(-5,4)#

#A'B=sqrt((4-1)^2+(-5+3)^2)=sqrt(9+4)=sqrt13#

#"change in distance "=sqrt65-sqrt13~~4.457" 3 dec. places"#

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Answer from HIX Tutor

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