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?

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Answer 1 · 2016-03-05T03:58:41

The new Point $A(4, -9)$
Difference $=d_n-d_o=sqrt82-4sqrt2=5.65685$

Original distance between point A and B
$d_o=sqrt((x_a-x_b)^2+(y_a-y_b)^2)$
$d_o=sqrt((-9--5)^2+(-4--8)^2)$
$d_o=sqrt((-4)^2+(4)^2)$
$d_o=4sqrt2$

the new distance $d_n$

Let $A(x_a, y_a)=(4, -9)$
$d_n=sqrt((x_a-x_b)^2+(y_a-y_b)^2)$

$d_n=sqrt((4--5)^2+(-9--8)^2)$
$d_n=sqrt((9)^2+(-1)^2)$
$d_n=sqrt(82)$

Difference $=d_n-d_o=sqrt82-4sqrt2=5.65685$

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

Point A is at (-9 ,-4 )(-9 ,-4 ) and point B is at (-5 ,-8 )(-5 ,-8 ). Point A is rotated (3pi)/2 (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?