Points A and B are at $(2, 9)$ $(2 ,9 )$ and $(8, 6)$ $(8 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?

Question

Points A and B are at $(2, 9)$ $(2 ,9 )$ and $(8, 6)$ $(8 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?

1 Answer

Impact of this question

1229 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-05T14:21:01

$C = (- \frac{16}{3}, - 14)$ $C=(-16/3,-14)$

Explanation:

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

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

$rArrA(2,9)toA'(-2,-9)" where A' is the image of A"$

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

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

$rArrulb-ulc=4ula'-4ulc$

$rArr3ulc=4ula'-ulb$

$color(white)(rArr3ulc)=4((-2),(-9))-((8),(6))$

$color(white)(rArr3ulc)=((-8),(-36))-((8),(6))=((-16),(-42))$

$rArrulc=1/3((-16),(-42))=((-16/3),(-14))$

$rArrC=(-16/3,-14)$

Science

Math

Humanities

... and beyond

Points A and B are at $(2, 9)$ $(2 ,9 )$ and $(8, 6)$ $(8 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Points A and B are at (2 ,9 )(2,9)(2 ,9 ) and (8 ,6 )(8,6)(8 ,6 ), respectively. Point A is rotated counterclockwise about the origin by pi πpi 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:

Related questions

Impact of this question

Points A and B are at $(2, 9)$ $(2 ,9 )$ and $(8, 6)$ $(8 ,6 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?