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
Jim G.
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

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