Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(2, 4)$ $(2 ,4 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ and dilated about point C by a factor of $4$ $4$ . If point A is now at point B, what are the coordinates of point C?

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Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(2, 4)$ $(2 ,4 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ and dilated about point C by a factor of $4$ $4$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-06-30T17:59:54

$C = (- 10, \frac{8}{3})$ $C=(-10,8/3)$

Explanation:

$under a counterclockwise rotation about the origin of \frac{π}{2}$ $"under a counterclockwise rotation about the origin of "pi/2$

$∙ a point (x, y) \to (- y, x)$ $• " a point "(x,y)to(-y,x)$

$A(3,7)toA'(-7,3)" where A' is the image of A"$

$vec(CB)=color(red)(4)vec(CA')$

$ulb-ulc=4(ula'-ulc)$

$ulb-ulc=4ula'-4ulc$

$3ulc=4ula'-ulb$

$color(white)(3ulc)=4((-7),(3))-((2),(4))$

$color(white)(3ulc)=((-28),(12))-((2),(4))=((-30),(8))$

$ulc=1/3((-30),(8))=((-10),(8/3))$

$rArrC=(-10,8/3)$

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Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(2, 4)$ $(2 ,4 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ and dilated about point C by a factor of $4$ $4$ . If point A is now at point B, what are the coordinates of point C?

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Points A and B are at (3 ,7 )(3,7)(3 ,7 ) and (2 ,4 )(2,4)(2 ,4 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 π2pi/2 and dilated about point C by a factor of 4 44 . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

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Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(2, 4)$ $(2 ,4 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ and dilated about point C by a factor of $4$ $4$ . If point A is now at point B, what are the coordinates of point C?