Question

in the coordinate plane, (overline{rs}) is the image of (overline{rs}) after a dilation with a scale factor of 1.2 centered at ((0, -6)). (rs) has endpoints (r(-6, -1)) and (s(6, 8)). what is the length of (overline{rs})? write your answer as a whole number or decimal rounded to the nearest tenth. (square) units

Explanation:

Step1: Find length of \( \overline{R'S'} \)

Use distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) for \( R'(-6, -1) \) and \( S'(6, 8) \).
\( d = \sqrt{(6 - (-6))^2 + (8 - (-1))^2} = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15 \)

Step2: Relate to \( \overline{RS} \) using scale factor

Dilation scale factor \( k = 1.2 \), so \( \text{Length of } \overline{R'S'} = k \times \text{Length of } \overline{RS} \).
Let \( L = \text{Length of } \overline{RS} \), then \( 15 = 1.2L \).

Step3: Solve for \( L \)

\( L = \frac{15}{1.2} = 12.5 \)

Answer:

12.5