Question

Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:

Answer 1

Answer: The answer is (c) $\dfrac{1}{2}.$

Step-by-step explanation: We are given the dilation of octagon ABCDEFGH which forms the octagon A'B'C'D'E'F'G'H' as shown in the given figure. Origin is the centre of dilation. We are to find the scale factor of the dilation.

We know that, to find the scale factor, we need to divide the length of one side of the dilated octagon A'B'C'D'E'F'G'H' by the length of the corresponding side of the original octagon ABCDEFGH.

Also, from the figure, we note that

GH = 4 units and G'H' = 2 units.

Therefore, the scale factor will be

$S=\dfrac{G'H'}{GH}=\dfrac{2}{4}=\dfrac{1}{2}.$

Thus, (c) is the correct option.

Answer 2

We can take out one of the points such as H (2,6) and then take it's dilation H' (1,3)and see that 2 and 6 were both multiplied by 1/2 to get 1 and 3, so the scale factor is 1/2