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
