How do you describe the translation of circle $(x - 1) 2 + (y - 4) 2 = 25$ $(x - 1)2 + (y - 4)2 = 25$ that results in an image whose equation is $(x + 1) 2 + (y - 5) 2 = 25$ $(x + 1)2 + (y - 5)2 = 25$ ?

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How do you describe the translation of circle $(x - 1) 2 + (y - 4) 2 = 25$ $(x - 1)2 + (y - 4)2 = 25$ that results in an image whose equation is $(x + 1) 2 + (y - 5) 2 = 25$ $(x + 1)2 + (y - 5)2 = 25$ ?

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Answer 1 · 2016-03-23T12:15:09

$((-2),(1))$

Explanation:

Compare the given equations to the standard equation.

$(x - a)^2 + (y - b)^2 = r^2$

where (a,b) are the coords of centre and r , is the radius.

so $(x-1)^2 + (y-4)^2 = 25 " has centre (1,4)and r =5"$

and $(x+1)^2 + (y-5)^2 = 25" has centre (-1,5) and r = 5 "$

Under a translation the circle retains it's shape, but position is changed.
Just need to consider how the centres have changed.

that is : (1,4) → (-1,5) and as a translation $((-2),(1))$

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How do you describe the translation of circle $(x - 1) 2 + (y - 4) 2 = 25$ $(x - 1)2 + (y - 4)2 = 25$ that results in an image whose equation is $(x + 1) 2 + (y - 5) 2 = 25$ $(x + 1)2 + (y - 5)2 = 25$ ?

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Explanation:

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Math

Humanities

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How do you describe the translation of circle (x - 1)2 + (y - 4)2 = 25(x−1)2+(y−4)2=25(x - 1)2 + (y - 4)2 = 25 that results in an image whose equation is (x + 1)2 + (y - 5)2 = 25(x+1)2+(y−5)2=25(x + 1)2 + (y - 5)2 = 25?

1 Answer

Explanation:

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Impact of this question

How do you describe the translation of circle $(x - 1) 2 + (y - 4) 2 = 25$ $(x - 1)2 + (y - 4)2 = 25$ that results in an image whose equation is $(x + 1) 2 + (y - 5) 2 = 25$ $(x + 1)2 + (y - 5)2 = 25$ ?