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

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Answer 1 · 2017-08-10T09:17:40

The coordinates of point $C = (- 21, 8)$ $C=(-21,8)$

Point $A=((6),(7))$ and point $B=((7),(4))$

The rotation of point $A$ counterclockwise tranforms the point $A$ into

$A'=((-7),(6))$

Let point $C=((x),(y))$

The dilatation is

$vec(CB)=2vec(CA')$

$((7),(4))-((x),(y))=2*((-7),(6))-((x),(y)))$

Therefore,

$7-x=2(-7-x)$

$7-x=-14-2x$

$x=-14-7=-21$

$4-y=2(6-y)$

$4-y=12-2y$

$y=12-4=8$

The point $C=(-21,8)$

Points A and B are at (6 ,7 )(6,7)(6 ,7 ) and (7 ,4 )(7,4)(7 ,4 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 π2pi/2 and dilated about point C by a factor of 2 22 . If point A is now at point B, what are the coordinates of point C?