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}) passes through point m. the slopes of (overline{no}) and (overline{no}) are the same or different.

Explanation:

Step1: Recall Dilation Properties

Dilation is a similarity transformation. When a figure is dilated with a center, the lines connecting corresponding points (like \( \overline{NO} \) and \( \overline{N'O'} \)) are collinear with the center of dilation (point \( M \)). Also, dilations preserve the slope of lines, meaning corresponding lines are parallel (or coincident, hence same slope).

Step2: Analyze Slope Relationship

Since \( \overline{NO} \) and \( \overline{N'O'} \) are collinear (because dilation from \( M \) makes them lie on the same line through \( M \)), their slopes must be equal (same).

Answer:

the same