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?
1 Answer
Feb 7, 2018
Explanation:
"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"
