Answer :
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 0.5
- The 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 rule
The 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 slope
Calculating 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:
https://brainly.com/question/2700001
Answer:
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
✔ (–1, 2)
.
The coordinates of M' in the image are
✔ (1, 2)
.
The length, L'M', is
✔ 2
.
The slope of the original segment and dilated segment are
✔ both zero
.
Step-by-step explanation: