Point A is at #(3 ,7 )# 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
Jun 1, 2016
(7 ,-3) , ≈ 8.944
Explanation:
The first step is to find the new coordinates of point A , which I will name A'.
Under a clockwise rotation about O of
#pi/2# a point (x ,y) → (y ,-x)
hence A (3 ,7) → A' (7 ,-3)
To calculate the change in length of AB with A'B use 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 points"# Length of AB using A(3 ,7) and B(5 ,-4)
#d_(AB)=sqrt((5-3)^2+(-4-7)^2)=sqrt125≈11.18# Length of A'B using A'(7 ,-3) and B(5 ,-4)
#d_(A'B)=sqrt((5-7)^2+(-4+3)^2)=sqrt5≈2.236# change in length = 11.18 - 2.236 = 8.944
