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,

If the center of dilation is at the origin, by what scale factor was octagon ABCDEFGH dilated? (4 points)

Question options:

1)

one half

2)

2

3)

4

4)

one quarter

2)  2

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Dilation is the enlargement or reduction of the size of an object. If a figure with point A(x, y) is dilated by a scale factor of k about the center of the origin, the new point would be at (kx, ky). If k < 1 it is a reduction and if k > 1 it is an enlargement.

The octagon ABCDEFGH has vertices at A(3, 1), B(3, -1), C(1, -3), D(1, -3), E(-3, -1), F(-3, 1), G(-1,3) and H(1, 3)

Octagon ABCDEFGH is then dilated about the origin to form octagon A'B'C'D'E'F'G'H' with vertices at A'(6, 2), B'(6, -2), C'(2, -6), D'(2, -6), E'(-6, -2), F'(-6, 2), G'(-2,6) and H'(2, 6)

A = (3, 1) and A' = (6, 2) = [2(3), 2(1)]

Therefore octagon ABCDEFGH was dilated by a scale factor of 2 to form octagon A'B'C'D'E'F'G'H'

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