Question

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 1

first we write the equation of the incial circle

general equation is

`(x+a)^2+(y+b)^2=r^2`

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

`\begin{gathered} (x-2)^2+(y-0)^2=2^2 \\ \\ (x-2)^2+y^2=2^2 \end{gathered}`

now apply the trasnformations

(x+4 , y-1)

we add 4 to x and subtrat 1 to y

`\begin{gathered} (x-2+4)^2+(y-1)^2=2^2 \\ \\ (x+2)^2+(y-1)^2=2^2 \end{gathered}`

dilation of 1/2

multiply the radious by the dilation

`(x+2)^2+(y-1)^2=(2*(1)/(2))^2`

Finally the equation of the new circle is

`(x+2)^2+(y-1)^2=1`