Points A and B are at $(3 ,6 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $5$ . 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 $(3 ,6 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $5$ . If point A is now at point B, what are the coordinates of point C?

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Answer 1 · 2018-06-11T20:44:19

$C=(-11/2,-35/4)$

Explanation:

$"under a counterclockwise rotation about the origin of "pi$

$• " a point "(x,y)to(-x,-y)$

$A(3,6)toA'(-3,-6)" where A' is the image of A"$

$vec(CB)=color(red)(5)vec(CA')$

$ulb-ulc=5(ula'-ulc)$

$ulb-ulc=5ula'-5ulc$

$4ulc=5ula'-ulb$

$color(white)(4ulc)=5((-3),(-6))-((7),(5))$

$color(white)(4ulc)=((-15),(-30))-((7),(5))=((-22),(-35))$

$ulc=1/4((-22),(-35))=((-11/2),(-35/4))$

$rArrC=(-11/2,-35/4)$

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Points A and B are at $(3 ,6 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $5$ . If point A is now at point B, what are the coordinates of point C?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Points A and B are at (3 ,6 )(3 ,6 ) and (7 ,5 )(7 ,5 ), respectively. Point A is rotated counterclockwise about the origin by pi pi and dilated about point C by a factor of 5 5 . 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 $(3 ,6 )$ and $(7 ,5 )$ , respectively. Point A is rotated counterclockwise about the origin by $pi$ and dilated about point C by a factor of $5$ . If point A is now at point B, what are the coordinates of point C?