Octagon abcdefgh and its dilation, octagon a'b'c'd'e'f'g'h', are shown on the coordinate plane below: octagon abcdefgh with ordered pairs at a at 3, 1, at b 3, negative 1, c 1, negative 3, d negative 1, negative 3, e negative 3, negative 1, f negative 3, 1, g negative 1, 3, h 1, 3. octagon a prime b prime c prime d prime e prime f prime g prime h prime with ordered pairs a prime 6, 2, at b prime 6, negative 2, at c prime 2, negative 6, at d prime negative 2, negative 6, at e prime negative 6, negative 2, at f prime negative 6, 2, at g prime negative 2, 6, at h prime 2, 6 if the center of dilation is at the origin, by what scale factor was octagon abcdefgh dilated? one half 2 4 one quarter

The correct option is 2. The scale factor of dilation is 2.

Step-by-step explanation:

It is given that Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H'.

The center of dilation is origin.

Let the scale factor is k.

If a figure dilated with scale factor k and center at origin, then

The coordinate of A are (3,1) and coordinates of A' are (6,2).

Since scale factor is k and center of dilation is origin, therefore

Therefore scale factor of dilation is 2. Second option is correct.

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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