Question

5
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 { m ^ { \prime } n ^ { \prime } } \\) is

Explanation:

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

When a point \((x,y)\) is dilated by a scale factor \(k\) with the origin as the center of dilation, the new coordinates \((x',y')\) are given by \((kx,ky)\).
For point \(M(2,4)\), after dilation with \(k = 0.8\), \(M'=(0.8\times2,0.8\times4)=(1.6,3.2)\)
For point \(N(3,5)\), after dilation with \(k = 0.8\), \(N'=(0.8\times3,0.8\times5)=(2.4,4)\)

Step2: Use the slope formula

The slope formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
Here, \(x_1 = 1.6,y_1=3.2,x_2 = 2.4,y_2 = 4\)
\(m=\frac{4 - 3.2}{2.4-1.6}=\frac{0.8}{0.8}\)

Answer:

\(1\)