Question

What is the scale factor of ABC to XYZ?

Answer 1

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

the answer is the option C

$\frac{1}{5}$

Answer 2

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: $\frac{1}{5}$