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]
