Question

the triangle stu is a dilation of the triangle stu. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Explanation:

Step1: Find the length of \( ST \) and \( S'T' \)

• Coordinates of \( S(-10,0) \), \( T(-4,0) \), \( S'(-2,0) \), \( T'(-1,0) \)
• \( ST=\vert- 4-(-10)\vert=\vert-4 + 10\vert = 6 \)
• \( S'T'=\vert-1-(-2)\vert=\vert-1 + 2\vert=1 \)

Step2: Calculate the scale factor

• Scale factor \( k=\frac{S'T'}{ST} \)
• Substitute \( S'T' = 1 \) and \( ST = 6 \) into the formula: \( k=\frac{1}{6} \)

Answer:

\(\frac{1}{6}\)