Points A and B are at $(6, 5)$ $(6 ,5 )$ and $(7, 8)$ $(7 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ 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 $(6, 5)$ $(6 ,5 )$ and $(7, 8)$ $(7 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ 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

1412 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-21T14:24:28

$C = (- 17, 4)$ $C=(-17,4)$

Explanation:

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

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

$rArrA(6,5)toA'(-5,6)" where A' is the image of A"$

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

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

$rArrulb-ulc=2ula'-2ulc$

$rArrulc=2ula'-ulb$

$color(white)(rArrulc)=2((-5),(6))-((7),(8))$

$color(white)(rArrulc)=((-10),(12))-((7),(8))=((-17),(4))$

$rArrC=(-17,4)$

Science

Math

Humanities

... and beyond

Points A and B are at $(6, 5)$ $(6 ,5 )$ and $(7, 8)$ $(7 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ 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 (6 ,5 )(6,5)(6 ,5 ) and (7 ,8 )(7,8)(7 ,8 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 π2pi/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 $(6, 5)$ $(6 ,5 )$ and $(7, 8)$ $(7 ,8 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ 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?