Question

The dashed triangle is a dilation image of the solid triangle. What is the scale factor?

A coordinate grid shows both the x- and y-axes from -10 to 10 and the graphs of a solid triangle and a dashed triangle.
The solid triangle has vertices at
left parenthesis 4 comma 4 right parenthesis and
left parenthesis 8 comma negative 4 right parenthesis and
left parenthesis negative 4 comma 4 right parenthesis.

The dashed triangle has vertices at
left parenthesis 2 comma 2 right parenthesis and
left parenthesis 4 comma negative 2 right parenthesis and
left parenthesis negative 2 comma 2 right parenthesis.

(1 point)
Responses

one-fourth
Image with alt text: one-fourth

one-half
Image with alt text: one-half

start fraction 2 over 3 end fraction
Image with alt text: start fraction 2 over 3 end fraction

2
2
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Answer 1

To find the scale factor, we can compare the corresponding side lengths of the solid triangle and the dashed triangle.

The first side of the solid triangle has a length of √((8-4)^2 + (-4-4)^2) = √(16+64) = √80.
The corresponding side of the dashed triangle has a length of √((4-2)^2 + (-2-2)^2) = √(4+16) = √20.

The scale factor can be found by dividing the length of the corresponding side of the dashed triangle by the length of the corresponding side of the solid triangle:

Scale factor = √20 / √80

Simplifying this ratio, we have:

Scale factor = √(20/80) = √(1/4) = 1/2

Therefore, the scale factor is one-half.