# Point A is at (3 ,2 ) and point B is at (3 ,-8 ). 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 10, 2016

The new A is $\left(2 , - 3\right)$ and the difference in the distance is approximately $4.9$.

#### Explanation:

A $\frac{\pi}{2}$ or $90$ degrees clockwise rotation of a point can be written as $\left(x , y\right) \to \left(y , - x\right)$.

So, $\left(3 , 2\right)$ rotated $\frac{\pi}{2}$ clockwise becomes $\left(2 , - 3\right)$.

The distance between the original point A (3,2) and B (3,-8) can be found using the distance formula.

sqrt((3-3)^2+(-8-2)^2$= \sqrt{{\left(- 10\right)}^{2}}$$= \sqrt{100}$$= 10$

The distance between the new point A (2,-3) and B (3,-8) is

$\sqrt{{\left(3 - 2\right)}^{2} + {\left(- 8 - - 3\right)}^{2}}$$= \sqrt{{1}^{2} + {\left(- 5\right)}^{2}}$$= \sqrt{1 + 25}$$= \sqrt{26}$$\cong 5.1$

The difference between the A and B changes by approximately $10 - 5.1 = 4.9$