# Point A is at #(4 ,1 )# and point B is at #(-9 ,-7 )#. Point A is rotated #(3pi)/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

May 19, 2016

(-1 ,4) and ≈ 1.664

#### Explanation:

Under a rotation of

#(3pi)/2" clockwise about the origin"# A point (x ,y) → (-y ,x)

Hence point A(4 ,1) → A'(-1 ,4)

We now require to calculate the distance between A and B and between A' and B.

We can do this 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"#

For A to Blet# (x_1,y_1)=(4 ,1)" and " (x_2,y_2)=(-9 ,-7)#

#d=sqrt((-9-4)^2+(-7-1)^2)=sqrt(169+64)≈15.264#

For A' to B#(x_1,y_1)=(-1 ,4)" and " (x_2,y_2)=(-9 ,-7)#

#d=sqrt((-9+1)^2+(-7-4)^2)=sqrt(64+121)≈13.60# The difference in distance = 15.264 - 13.60 = 1.664