# Point A is at #(3 ,-2 )# and point B is at #(2 ,1 )#. Point A is rotated #pi # 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 14, 2016

≈ 1.937

#### Explanation:

Under a rotation of

#pi " about the origin " # a point (x , y) → (-x , -y)

hence A(3 , -2) → (-3 , 2)

Now , we have to calculate the difference between 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 coordinate points "# For length AB, let

#(x_1,y_1)=(3,-2)" and " (x_2,y_2)=(2,1)#

# d_(AB) = sqrt((2-3)^2 + (1+2)^2) = sqrt(1+9) = sqrt10 ≈ 3.162# For length A'B, let

#(x_1,y_1)=(-3,2)" and " (x_2,y_2)=(2,1)#

#d_(A'B) = sqrt((2+3)^2 + (1-2)^2) = sqrt(25+1)=sqrt26 ≈ 5.099# difference = A'B - AB = 5.099 - 3.162 = 1.937