# Point A is at (-7 ,7 ) and point B is at (5 ,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?

Feb 7, 2018

New coordinates of A are $\textcolor{red}{7 , - 7}$

Change ( reduction ) in length of $\vec{A B}$ due to the rotation :

$\textcolor{g r e e n}{\vec{A B} - \vec{A ' B} = 13.42 - 8.25 = 5.17}$

#### Explanation:

Given : A (-7, 7), B (5, 1). Rotated clockwise by $\pi$ about the origin.

$A \left(\begin{matrix}- 7 \\ 7\end{matrix}\right) \to A ' \left(\begin{matrix}7 \\ - 7\end{matrix}\right)$

New coordinates of A are $\textcolor{red}{7 , - 7}$

$\vec{A B} = \sqrt{{\left(- 7 - 5\right)}^{2} + {\left(7 - 1\right)}^{2}} \approx \textcolor{b l u e}{13.42}$

$\vec{A ' B} = \sqrt{{\left(7 - 5\right)}^{2} + {\left(- 7 - 1\right)}^{2}} \approx \textcolor{b l u e}{8.25}$

Change (reduction) in length of $\vec{A B}$ due to the rotation :

$\textcolor{g r e e n}{\vec{A B} - \vec{A ' B} = 13.42 - 8.25 = 5.17}$