Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(4, 2)$ $(4 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?

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Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(4, 2)$ $(4 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?

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Answer 1 · 2018-01-13T09:57:27

After Point A is rotated counterclockwise about the origin by $π$ $pi$ , its new coordinates are $(- 3, - 7)$ $(-3, -7)$ .

The difference between the $x$ $x$ coordinates of Point A and B now is $4 - (- 3) = 7$ $4-(-3)=7$ and $y$ $y$ coordinates: $2 - (- 7) = 9$ $2-(-7)=9$

Since Point A was dilated about Point C by a factor of 5, we can find out by how much the coordinates change with each integer increase in factor.

For the $x$ $x$ coordinate:
$\frac{7}{4} = 1.75$ $7/4=1.75$
and $y$ $y$ coordinate:
$\frac{9}{4} = 2.25$ $9/4=2.25$

So for every integer increase in factor, the point moves 1.75 to the right and 2.25 upwards.

Point C is therefore
$(- 3 - 1.75, - 7 - 2.25)$ $(-3-1.75, -7-2.25)$
$= (- 4.75, - 9.25)$ $=(-4.75, -9.25)$

Answer 2 · 2018-01-13T11:24:09

$C = (- \frac{19}{4}, - \frac{37}{4})$ $C=(-19/4,-37/4)$

Explanation:

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

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

$rArrA(3,7)toA'(-3,-7)" where A' is the image of A"$

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

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

$rArrulb-ulc=5ula'-5ulc$

$rArr4ulc=5ula'-ulb$

$color(white)(4ulcxx)=5((-3),(-7))-((4),(2))$

$color(white)(xxxx)=((-15),(-35))-((4),(2))=((-19),(-37))$

$rArrulc=1/4((-19),(-37))=((-19/4),(-37/4))$

$rArrC=(-19/4,-37/4)$

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Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(4, 2)$ $(4 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?

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Explanation:

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Points A and B are at (3 ,7 )(3,7)(3 ,7 ) and (4 ,2 )(4,2)(4 ,2 ), respectively. Point A is rotated counterclockwise about the origin by pi πpi and dilated about point C by a factor of 5 55 . If point A is now at point B, what are the coordinates of point C?

2 Answers

Explanation:

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Points A and B are at $(3, 7)$ $(3 ,7 )$ and $(4, 2)$ $(4 ,2 )$ , respectively. Point A is rotated counterclockwise about the origin by $π$ $pi$ 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?