Respuesta :

calculista

we know that

Triangles ABC and XYZ are similar

so

The ratio of the corresponding sides are equal, and this ratio is called the scale factor

[tex]\frac{XY}{AB}= \frac{YZ}{BC}= \frac{XZ}{AC}[/tex]

substitute the values

[tex]\frac{9}{45}= \frac{12}{60}= \frac{7}{35}= \frac{1}{5}[/tex]

therefore

the answer is the option C

[tex]\frac{1}{5}[/tex]

Answer:

Option C is correct.

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Scale factor is defined as the ratio of the image

In triangle ABC and triangle XYZ:

[tex]\angle A = \angle X = 96^{\circ}[/tex]   [Angle]

[tex]\angle B = \angle Y = 35^{\circ}[/tex]   [Angle]

AA similarity states that  the two triangles have the corresponding angles that are equal in measure.

by AA  similarity we have;

Triangle ABC and triangle XYZ are similar.

Then by definition of similar triangles:

Corresponding sides are in proportion:

[tex]\frac{AB}{XY}=\frac{BC}{YZ} = \frac{AC}{XZ}[/tex]

Scale factor: The reduced ratio of two corresponding sides of a given triangles.

then;

[tex]\frac{AB}{XY} = \frac{1}{k}[/tex]

Substitute the given values:

[tex]\frac{45}{9} = \frac{1}{k}[/tex]

Simplify

[tex]\frac{1}{k} =5[/tex]

or

[tex]k = \frac{1}{5}[/tex]

Therefore, the scale factor of triangle ABC to triangle XYZ is: [tex]\frac{1}{5}[/tex]

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