Points A and B are at $(4 ,6 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi/2$ and dilated about point C by a factor of $1/2$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-06-08T02:25:06

$color(green)("Coordinates of " C = (5,(3/2))$

$A(4,6), B(7,5), "counterclockwise rotation "$ pi/2 $, "dilation factor" 1/2$

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

New coordinates of A after $(3pi)/2$ counterclockwise rotation

$A(4,6) rarr A' (-6,4)$

$vec (BC) = (1/2) vec(A'C)$

$b - c = (1/2)a' - (1/2)c$

$(1/2)c = -(1/2)a' + b$

$(1/2)C((x),(y)) = -(1/2)((-6),(4)) + ((7),(5)) = ((10),(3))$

$color(green)("Coordinates of " 2 *C ((10),3) = C(5,(3/2))$

Points A and B are at (4 ,6 )(4 ,6 ) and (7 ,5 )(7 ,5 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 pi/2 and dilated about point C by a factor of 1/2 1/2 . If point A is now at point B, what are the coordinates of point C?