# 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#