# 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 ABlet

# (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'Blet

# (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