# Point A is at (-9 ,-4 ) and point B is at (-5 ,-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?

The new Point $A \left(4 , - 9\right)$
Difference $= {d}_{n} - {d}_{o} = \sqrt{82} - 4 \sqrt{2} = 5.65685$

#### Explanation:

Original distance between point A and B
${d}_{o} = \sqrt{{\left({x}_{a} - {x}_{b}\right)}^{2} + {\left({y}_{a} - {y}_{b}\right)}^{2}}$
${d}_{o} = \sqrt{{\left(- 9 - - 5\right)}^{2} + {\left(- 4 - - 8\right)}^{2}}$
${d}_{o} = \sqrt{{\left(- 4\right)}^{2} + {\left(4\right)}^{2}}$
${d}_{o} = 4 \sqrt{2}$

the new distance ${d}_{n}$

Let $A \left({x}_{a} , {y}_{a}\right) = \left(4 , - 9\right)$
${d}_{n} = \sqrt{{\left({x}_{a} - {x}_{b}\right)}^{2} + {\left({y}_{a} - {y}_{b}\right)}^{2}}$

${d}_{n} = \sqrt{{\left(4 - - 5\right)}^{2} + {\left(- 9 - - 8\right)}^{2}}$
${d}_{n} = \sqrt{{\left(9\right)}^{2} + {\left(- 1\right)}^{2}}$
${d}_{n} = \sqrt{82}$

Difference $= {d}_{n} - {d}_{o} = \sqrt{82} - 4 \sqrt{2} = 5.65685$

God bless....I hope the explanation is useful.