Question

Point A is at `(7 ,-1 )` and point B is at `(-8 ,-2 )`. 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?

Answer 1

(1 ,7), ≈ 2.305

Explanation:

Let's calculate the distance between A and B to begin with 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"`

The 2 points here are(7 ,-1) and (-8 ,-2)

let `(x_1,y_1)=(7,-1)" and " (x_2,y_2)=(-8,-2)`

`d=sqrt((-8-7)^2+(-2+1)^2)=sqrt(225+1)≈15.033`

Under a rotation about the origin of `pi/2`

a point (x ,y) → (-y ,x)

`rArrA(7,-1)to(1,7)`

Now calculate the distance between (1 ,7) and (-8 ,-2)

`d=sqrt((-8-1)^2+(-2-7)^2)=sqrt(81+81)≈12.728`

change in distance between A and B = 15.033 - 12.728

`=2.305`