# 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?

Sep 21, 2016

(1 ,7), ≈ 2.305

#### Explanation:

Let's calculate the distance between A and B to begin with using the $\textcolor{b l u e}{\text{distance formula}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points}$

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

let $\left({x}_{1} , {y}_{1}\right) = \left(7 , - 1\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 8 , - 2\right)$

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

Under a rotation about the origin of $\frac{\pi}{2}$

a point (x ,y) → (-y ,x)

$\Rightarrow A \left(7 , - 1\right) \to \left(1 , 7\right)$

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

$= 2.305$