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1 2 Q8 (x - 3)2 + (v +0.5)2 = 1 The result of a transformation of circle A using the rule (x,y) → (1 +4, y - 1), followed by a dilation of centered at the origin will result in which crcle (x - 2)2 + 12 = 4 from the choices below? (x + 2)2 + (1 - 1)2 = 4 (x + 1)2 + (1 -0.5)2 = 2 A



Answer :

first we write the equation of the incial circle

general equation is

[tex](x+a)^2+(y+b)^2=r^2[/tex]

where (-a,-b) is the origin and r the radious

From the graph, the origin is (2,0) and radious 2 units

then the equation is

[tex]\begin{gathered} (x-2)^2+(y-0)^2=2^2 \\ \\ (x-2)^2+y^2=2^2 \end{gathered}[/tex]

now apply the trasnformations

(x+4 , y-1)

we add 4 to x and subtrat 1 to y

[tex]\begin{gathered} (x-2+4)^2+(y-1)^2=2^2 \\ \\ (x+2)^2+(y-1)^2=2^2 \end{gathered}[/tex]

dilation of 1/2

multiply the radious by the dilation

[tex](x+2)^2+(y-1)^2=(2\times\frac{1}{2})^2[/tex]

Finally the equation of the new circle is

[tex](x+2)^2+(y-1)^2=1[/tex]

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