The rule DO,0.25 (x, y) → (0.25x, 0.25y) is applied to the segment LM to make an image of segment L'M', not shown. The coordinates of L' in the image are . The coordinates of M' in the image are . The length, L'M', is . The slope of the original segment and dilated segment are .

When a line segment is dilated, the original line segment and the new line segment will have the same slope. The coordinate of L' is (-0.25,0.5)The coordinate of M' is (0.25,0.5)The length of L'M' is 0.5The slope of the original segment and the dilated segment are 0.Given that:[tex]D_O, 0.25(x, y) \to (0.25x, 0.25y)[/tex] --- the dilation ruleThe coordinates of L and M are:[tex]L = (-1,2)[/tex] [tex]M = (1,2)[/tex]To calculate the coordinates of L' and M', we simply multiply the scale of dilation by the coordinates of L and M.[tex]D_O, 0.25(x, y) \to (0.25x, 0.25y)[/tex] means that the scale of dilation (k) is 0.25.So, we have:[tex]L' = 0.25 \times L[/tex][tex]L' = 0.25 \times (-1,2)[/tex][tex]L' = (0.25 \times -1,0.25 \times2)[/tex][tex]L' = (-0.25,0.5)[/tex]Similarly[tex]M' = 0.25 \times M[/tex][tex]M' = 0.25 \times (1,2)[/tex][tex]M' = (0.25 \times 1,0.25 \times 2)[/tex][tex]M' = (0.25,0.5)[/tex]The length L'M' is calculated using distance formula:[tex]L'M' = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Where:[tex]L' = (-0.25,0.5)[/tex] --- [tex](x_1,y_1)[/tex][tex]M' = (0.25,0.5)[/tex] --- [tex](x_2,y_2)[/tex]So, we have:[tex]L'M' = \sqrt{(0.25 --0.25)^2 + (0.5 - 0.5)^2}[/tex][tex]L'M' = \sqrt{(0.5)^2 + (0)^2}[/tex][tex]L'M' = \sqrt{0.5^2}[/tex][tex]L'M' = 0.5[/tex]Hence, the length of L'M' is 0.5 units.The slope (m) of a line is calculated using:[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Dilation doesn't change the slope of a line. So, LM and L'M' will have the same slopeCalculating the slope of L'M', we have:[tex]m = \frac{0.5 - 0.5}{0.25 -- 0.25}[/tex][tex]m = \frac{0}{0.5}[/tex][tex]m = 0[/tex]Hence, the slope of both lines is 0.Read more about dilations at: