Points A and B are at $(9 ,7 )$ and $(4 ,3 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $3$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2016-10-02T21:17:06

$C = (-31/3, -8)$

Let's begin by rotating point A:

$r = sqrt(9² + 7²)$

$r = sqrt(81 + 49)$

$r = sqrt130$

$theta = tan^-1(7/9) + pi$

The new point A is:

$(sqrt130cos(tan^-1(7/9) + pi), sqrt130sin(tan^-1(7/9) + pi))$

$(-9, -7)$

$4 = 3(9 - C_x)$

$3 = 3(7 - C_y)$

$C_x = -9 - 4/3 = -31/3$

$C_y = -7 - 1 = -8$

$C = (-31/3, -8)$

Points A and B are at (9 ,7 )(9 ,7 ) and (4 ,3 )(4 ,3 ), respectively. Point A is rotated counterclockwise about the origin by pi pi and dilated about point C by a factor of 3 3 . If point A is now at point B, what are the coordinates of point C?