Point A is at #(-1 ,-8 )# and point B is at #(-5 ,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?

Question

Point A is at #(-1   ,-8  )# and point B is at #(-5  ,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?

Theodore Abad · Accepted Answer

(-8 ,1) and ≈ 8.104

Under a rotation of #pi/2# clockwise about O. a point (x ,y) → (y ,-x) hence point A(-1 ,-8) → A' (-8 ,1) To find the change in distance between AB and A'B we require to calculate the length of AB and A'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"# length of AB# (x_1,y_1)=(-1 ,-8)" and " (x_2,y_2)=(-5,3)# #d_(AB)=sqrt((-5+1)^2+(3+8)^2)=sqrt(16+121)≈11.705# length of A'B #(x_1,y_1)=(-8 ,1)" and " (x_2,y_2)=(-5, 3)# #d_(A'B)=sqrt((-5+8)^2+(3-1)^2)=sqrt(9+4)≈3.601# hence the change in length = 11.705 - 3.601 = 8.104

Mason Adams · Answer

undefined The new coordinates of point A after rotating π/2 radians clockwise about the origin are (8, -1). The distance between points A and B has changed by 10 units.