Point A is at (9 ,-2 ) and point B is at (1 ,-3 ). 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
Apr 25, 2016
(-2 ,-9) , ≈ 1.13
Explanation:
Under a rotation of
pi/2" clockwise about 0 " a point (x ,y) → (y ,-x)
hence A (9 ,-2) → A' (-2 , -9)
To calculate the change in distance we need to find the length of AB and A'B 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 points " calculate AB
let
(x_1,y_1)=(9,-2)" and " (x_2,y_2)=(1,-3)
d=sqrt((1-9)^2+(-3+2)^2)=sqrt(64+1)=sqrt65 ≈ 8.06 calculate A'B
let
(x_1,y_1)=(-2,-9)" and " (x_2,y_2)=(1,-3)
d=sqrt((1+2)^2+(-3+9)^2)=sqrt(9+36)=sqrt45 ≈ 6.93 change in length = 8.06 - 6.93 = 1.13
