15 points! What is the scale factor of the dilation?

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carlosego carlosego · Answer 1 · 2019-03-15T16:42:52+01:00

Answer: [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Use the formula for calculate the distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Calculate the distance AB. Substitute the coordinates into the formula. Then:

[tex]d_{AB}=\sqrt{(8-0)^2+(8-(-7))^2}[/tex]

[tex]d_{AB}=17[/tex]

Calculate the distance A'B'. Substitute the coordinates into the formula. Then:

[tex]d_{A'B'}=\sqrt{(2-6)^2+(1-5-(-6))^2}[/tex]

[tex]d_{A'B'}=\frac{17}{2}[/tex]

As you can see, the distance A'B' is the distance AB multiplied by 1/2. Therefore, this is the scale factor.

facundo3141592 facundo3141592 · Answer 2 · 2022-03-03T10:28:05+01:00

The scale of dilation is k = 0.5

The scale of dilation will be given by the quotient between the length A'B' and AB.

The endpoints of AB are.

(0, -7) and (8, 8).

So the distance of that segment is:

[tex]d = \sqrt{(0 - 8)^2 + (-7 - 8)^2} = 17[/tex]

For the dilated segment, the endpoints are:

(6, -6) and (2, 1.5)

So the distance is:

[tex]d' = \sqrt{(6 - 2)^2 + (-6 - 1.5)^2} = 8.5[/tex]

So the scale of dilation is:

k = 8.5/17 = 0.5

Because k is smaller than 1, it would be actually a contraction, not a dilation.

If you want to learn more about dilations, you can read:

https://brainly.com/question/3457976