Points A and B are at $(9, 2)$ $(9 ,2 )$ and $(1, 5)$ $(1 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?

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Answer 1 · 2018-06-08T02:19:59

$Coordinates of C ((\frac{7}{2}), - 11)$ $color(blue)("Coordinates of " C ((7/2),-11)$

$A (9, 2), B (1, 5), rotation$ $A(9,2), B(1,5), "rotation "$ (3pi)/2 $, dilation factor 3$ $, "dilation factor" 3$

![https://teacher.desmos.com/activitybuilder/custom/566b16af914c731d06ef1953]( useruploads.socratic.org )

New coordinates of A after $\frac{3 π}{2}$ $(3pi)/2$ counterclockwise rotation

$A(9,2) rarr A' (2,-9)$

$vec (BC) = 3 vec(A'C)$

$b - c = 3a' - 3c$

$2c = 3a' - b$

$2C((x),(y)) = 3((2),(-9)) + ((1),(5)) = ((7),(-22))$

$color(blue)("Coordinates of " (1/2)C ((7),-22) = C ((7/2),-11)$

Points A and B are at (9 ,2 )(9,2)(9 ,2 ) and (1 ,5 )(1,5)(1 ,5 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2(3pi)/2 and dilated about point C by a factor of 3 33 . If point A is now at point B, what are the coordinates of point C?