Points A and B are at $(7, 9)$ $(7 ,9 )$ and $(6, 8)$ $(6 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?

Question

Points A and B are at $(7, 9)$ $(7 ,9 )$ and $(6, 8)$ $(6 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?

1 Answer

Impact of this question

1383 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-27T14:37:42

$C = (12, - 22)$ $C=(12,-22)$

Explanation:

$under a counterclockwise rotation about the origin of \frac{3 π}{2}$ $"under a counterclockwise rotation about the origin of "(3pi)/2$

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

$A(7,9)toA'(9,-7)" where A' is the image of A"$

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

$ulb-ulc=2(ula'-ulc)$

$ulb-ulc=2ula'-2ulc$

$ulc=2ula'-ulb$

$color(white)(ulc)=2((9),(-7))-((6),(8))$

$color(white)(ulc)=((18),(-14))-((6),(8))=((12),(-22))$

$rArrC=(12,-22)$

Science

Math

Humanities

... and beyond

Points A and B are at $(7, 9)$ $(7 ,9 )$ and $(6, 8)$ $(6 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Points A and B are at (7 ,9 )(7,9)(7 ,9 ) and (6 ,8 )(6,8)(6 ,8 ), respectively. Point A is rotated counterclockwise about the origin by (3pi)/2 3π2(3pi)/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?

1 Answer

Explanation:

Related questions

Impact of this question

Points A and B are at $(7, 9)$ $(7 ,9 )$ and $(6, 8)$ $(6 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{3 π}{2}$ $(3pi)/2$ 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?