Question

select the correct answer from each drop-down menu.
polygon mnopq is dilated by a scale factor of 5.4 with point m as the center of dilation to form the image mnopq. compare \\(\overline{no}\\) and \\(\overline{no}\\).
\\(\overline{no}\\) drop-down menu with options passes, does not pass through point m. the slopes of \\(\overline{no}\\) and \\(\overline{no}\\) are drop-down menu.

Explanation:

Step1: Recall Dilation Properties

Dilation is a similarity transformation that preserves parallelism (so lines remain parallel, hence same slope) and collinearity with the center. Since \( M \) is the center of dilation, the line \( N'O' \) (image of \( NO \)) must pass through \( M \) (because dilation from \( M \) maps \( N \) to \( N' \) and \( O \) to \( O' \), so \( M \), \( N \), \( N' \) are colinear and \( M \), \( O \), \( O' \) are colinear, implying \( N'O' \) passes through \( M \)). Also, dilated lines are parallel to original, so slopes are equal.

Step2: Analyze First Dropdown

For the first dropdown (about \( \overline{N'O'} \) through \( M \)): By dilation's collinearity with center, \( \overline{N'O'} \) passes through \( M \).

Step3: Analyze Second Dropdown

For the slopes: Dilation preserves the slope (since it's a similarity transformation, parallel lines have equal slopes), so slopes of \( \overline{N'O'} \) and \( \overline{NO} \) are equal.

Answer:

First dropdown: passes
Second dropdown: equal