# Point A is at (8 ,-4 ) and point B is at (2 ,-3 ). 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?

Oct 29, 2016

A(8,-4)to(4,8)," change"≈5.097

#### Explanation:

Under a clockwise rotation about the origin of $\frac{3 \pi}{2}$

a point (x ,y) → (-y ,x)

Hence A (8 ,-4) → A(4 ,8)

To calculate the distance (d) between A and B use the $\textcolor{b l u e}{\text{distance formula}}$

color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)color(white)(2/2)|)))
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points}$

The 2 points here are A(8 ,-4) and B(2 ,-3). That is the original A and B.

let $\left({x}_{1} , {y}_{1}\right) = \left(8 , - 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(2 , - 3\right)$

d=sqrt((2-8)^2+(-3+4)^2)=sqrt37≈6.083

Now use the 'new' point A(4 ,8) and B(2 ,-3)

d=sqrt((2-4)^2+(-3-8)^2)=sqrt125≈11.180

change in distance between A and B = 11.180 - 6.083 = 5.097