# Point A is at (6 ,2 ) and point B is at (3 ,8 ). 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?

(-2,6) is the new coordinate of Point A
Now, the points are closer by 1.323

#### Explanation:

Origin $\left(0 , 0\right)$
Point A$\left(6 , 2\right)$
Point B$\left(3 , 8\right)$

Distance between points A and B is
sqrt((8-2)^2+(3-6)^2
=sqrt(6^2+3^2
=sqrt(36+9
$= \sqrt{45}$
$= 6.708$

After transformation
Rotation by $\frac{3 \pi}{2}$
When rotated by$\frac{\pi}{2}$
the new coordinates are $\left(2 , - 6\right)$
When further rotated by $\pi$
the coordinates are further transformed into -2,6)
$\left(- 2 , 6\right)$ is the transformed coordinate of the point A

After transformation
Point A$\left(- 2 , 6\right)$
Point B$\left(3 , 8\right)$

Distance after transformation is
sqrt((8-6)^2+(3-(-2))^2
=sqrt(2^2+5^2
=sqrt(4+25
$= \sqrt{29}$
$= 5.385$

The distance between the points A and B has changed by
$5.385 - 6.708 = - 1.323$

Now, the points are closer by 1.323