Points A and B are at $(5 ,8 )$ and $(7 ,3 )$ , 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?

Question

Points A and B are at $(5 ,8 )$ and $(7 ,3 )$ , 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

Impact of this question

1185 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-04T09:49:27

$C=(-8,-43/4)$

Explanation:

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

$• " a point "(x,y)to(-x,-y)$

$A(5,8)toA'(-5,-8)" where A' is the image of A"$

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

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

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

$4ulc=5ula'-ulb$

$color(white)(4ulc)=5((-5),(-8))-((7),(3))$

$color(white)(4ulc)=((-25),(-40))-((7),(3))=((-32),(-43))$

$ulc=1/4((-32),(-43))=((-8),(-43/4))$

$rArrC=(-8,-43/4)$

Science

Math

Humanities

... and beyond

Points A and B are at $(5 ,8 )$ and $(7 ,3 )$ , 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:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Points A and B are at (5 ,8 )(5 ,8 ) and (7 ,3 )(7 ,3 ), 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:

Related questions

Impact of this question

Points A and B are at $(5 ,8 )$ and $(7 ,3 )$ , 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?