Point A is at (7 ,-1 ) and point B is at (-8 ,-2 ). 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
Sep 21, 2016
(1 ,7), ≈ 2.305
Explanation:
Let's calculate the distance between A and B to begin with using the
color(blue)"distance formula"
color(red)(bar(ul(|color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(a/a)|)))
where(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points" The 2 points here are(7 ,-1) and (-8 ,-2)
let
(x_1,y_1)=(7,-1)" and " (x_2,y_2)=(-8,-2)
d=sqrt((-8-7)^2+(-2+1)^2)=sqrt(225+1)≈15.033 Under a rotation about the origin of
pi/2 a point (x ,y) → (-y ,x)
rArrA(7,-1)to(1,7) Now calculate the distance between (1 ,7) and (-8 ,-2)
d=sqrt((-8-1)^2+(-2-7)^2)=sqrt(81+81)≈12.728 change in distance between A and B = 15.033 - 12.728
=2.305
