Respuesta :

Answer:

[tex]\frac{1}{2}[/tex] , 3 , 3

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original

scale factor = [tex]\frac{K'M'}{KM}[/tex] = [tex]\frac{2.5}{5}[/tex] = [tex]\frac{1}{2}[/tex]

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scale factor = [tex]\frac{S'Q'}{SQ}[/tex] = [tex]\frac{6}{2}[/tex] = 3

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scale factor = [tex]\frac{L'H'}{LH}[/tex] = [tex]\frac{6}{3}[/tex] = 2

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semsee45

Answer:

a) Scale factor 2

b) Scale factor 0.5

c) Scale factor 3

Step-by-step explanation:

Dilation is a transformation that resizes a figure by a scale factor, maintaining the shape but altering its size.

To calculate the scale factor of dilation, divide the length of a side of the dilated image by the length of the corresponding side in the original pre-image.

Part a

In the given diagram, triangle H'I'J' is the image, and triangle HIJ is the pre-image. Given that H'I' = 6 and HI = 3, then:

[tex]\textsf{Scale factor}=\dfrac{H'I'}{HI}=\dfrac{6}{3}=2[/tex]

This means that the side lengths of triangle H'I'J' are twice as long as the corresponding side lengths of the triangle HIJ.

Part b

In the given diagram, triangle K'L'M' is the image, and triangle KLM is the pre-image. Given that K'M' = 2.5 and KM = 5, then:

[tex]\textsf{Scale factor}=\dfrac{K'M'}{KM}=\dfrac{2.5}{5}=0.5[/tex]

This means that the side lengths of triangle K'L'M' are half as long as the corresponding side lengths of the triangle KLM.

Part c

In the given diagram, triangle Q'R'S' is the image, and triangle QRS is the pre-image. Given that Q'S' = 6 and QS = 2, then:

[tex]\textsf{Scale factor}=\dfrac{Q'S'}{QS}=\dfrac{6}{2}=3[/tex]

This means that the side lengths of triangle Q'R'S' are three times as long as the corresponding side lengths of the triangle QRS.

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