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alexdok [17]
2 years ago
15

What is the scale factor of ABC to XYZ?

Mathematics
2 answers:
Blababa [14]2 years ago
8 0

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

\frac{XY}{AB}= \frac{YZ}{BC}= \frac{XZ}{AC}

substitute the values

\frac{9}{45}= \frac{12}{60}= \frac{7}{35}= \frac{1}{5}

therefore

<u>the answer is the option C</u>

\frac{1}{5}

Savatey [412]2 years ago
7 0

Answer:

Option C is correct.

\frac{1}{5}

Step-by-step explanation:

Scale factor is defined as the ratio of the image

In triangle ABC and triangle XYZ:

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

\angle B = \angle Y = 35^{\circ}   [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:

\frac{AB}{XY}=\frac{BC}{YZ} = \frac{AC}{XZ}

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

then;

\frac{AB}{XY} = \frac{1}{k}

Substitute the given values:

\frac{45}{9} = \frac{1}{k}

Simplify

\frac{1}{k} =5

or

k = \frac{1}{5}

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

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