Points A and B are at $(2, 9)$ $(2 ,9 )$ and $(3, 2)$ $(3 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ and dilated about point C by a factor of $3$ $3$ . 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 $(3, 2)$ $(3 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ and dilated about point C by a factor of $3$ $3$ . If point A is now at point B, what are the coordinates of point C?

1 Answer

Impact of this question

1247 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-05T18:52:25

$C = (- 15, 2)$ $C=(-15,2)$

Explanation:

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

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

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

$"Under a dilatation about " C" of factor 3"$

$vec(CB)=color(red)(3)vec(CA')$

$rArrulb-ulc=color(red)(3)(ula'-ulc)$

$rArrulb-ulc=3ula'-3ulc$

$rArr2ulc=3ula'-ulb$

$color(white)(rArr2cx)=3((-9),(2))-((3),(2))=((-30),(4))$

$rArrulc=1/2((-30),(4))=((-15),(2))$

$rArrC=(-15,2)$

Science

Math

Humanities

... and beyond

Points A and B are at $(2, 9)$ $(2 ,9 )$ and $(3, 2)$ $(3 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ and dilated about point C by a factor of $3$ $3$ . 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 (3 ,2 )(3,2)(3 ,2 ), respectively. Point A is rotated counterclockwise about the origin by pi/2 π2pi/2 and dilated about point C by a factor of 3 33 . 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 $(3, 2)$ $(3 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $\frac{π}{2}$ $pi/2$ and dilated about point C by a factor of $3$ $3$ . If point A is now at point B, what are the coordinates of point C?