Question

You can transform V to V' by translating it and then performing a dilation centered at V'. Find the translation rule and scale factor of the dilation.  Simplify the scale factor and write it as a proper fraction, improper fraction, or whole number.  Translation: (x, y) -> (___,___) Scale factor: ___​

Answer 1

Translation rule → (x + 10, y + 1)

Scale factor = 4

Explanation:

Coordinates of V → (-8, -2)

Coordinates of V' → (2, -1)

Therefore, point V has been translated from x = -8 to x = 2,

Translation on x-axis → 2 - (-8) = 10 units

Translation on y-axis → -1 - (-2) = -1 + 2

= 1 unit

If the point V is translated 10 units right and 1 unit upwards,

Rule for the translation → (x + 10, y + 1)

Radius of the circle V = 2 units

Radius of the circle V' = 8 units

Scale factor =
`\frac{\text{Dimension of the image}}{\text{Dimension of the original}}`

=
`\frac{\text{Radius of the image}}{\text{Radius of the original}}`

=
`(8)/(2)`

= 4

Therefore, circle V has been dilated by a scale factor of 4 to form circle V'.