Question

Find the translation rule and the scale factor of the dilation that transforms Ol to Ol'.

4))
9
A)
(x, y) -> (x + 7, y + 8); scale factor = 2
B)
(x, y) -> (x + 8, y + 7); scale factor = 2
C
(x, y) -> (x = 7, y + 8); scale factor = 3
Di
(x, y) -> (x = 8, y + 7): scale factor = 3

Answer 1

C (x, y) -> (x + 7, y + 8); scale factor = 3

Explanation:

The translation can be found by subtracting the coordinates of the original center from those of the center of the image. The scale factor will be the ratio of the radii.

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translation

We note the center coordinates are I(-3, -6) and I'(4, 2). Then the translation is ...

I' -I = (4, 2) -(-3, -6) = (4 +3, 2 +6) = (7, 8)

(x, y) ⇒ (x +7, y +8)

scale factor

The radius of each circle can be found by counting the grid squares from the center to the circle. It works best to do this along a horizontal or vertical line.

The radius of circle I is 2; the radius of circle I' is 6. The scale factor is ...

scale factor = 6/2 = 3