Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
polygon mnopq is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image mnopq. the coordinates of point m are (2, 4), and the coordinates of point n are (3, 5).
the slope of \\(\overline{mn}\\) is \\(square\\).

Explanation:

Step1: Find coordinates of \( M' \) and \( N' \)

To find the coordinates of a point after dilation with the origin as the center and a scale factor \( k \), we use the rule \( (x,y) \to (kx,ky) \). For point \( M(2,4) \) with \( k = 0.8 \), \( M'=(0.8\times2,0.8\times4)=(1.6,3.2) \). For point \( N(3,5) \) with \( k = 0.8 \), \( N'=(0.8\times3,0.8\times5)=(2.4,4) \).

Step2: Calculate the slope of \( \overline{M'N'} \)

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \( (x_1,y_1)=(1.6,3.2) \) and \( (x_2,y_2)=(2.4,4) \). Then \( m=\frac{4 - 3.2}{2.4 - 1.6}=\frac{0.8}{0.8}=1 \).

Answer:

\( 1 \)