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
Jim G.
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 B let (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

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