The question is incomplete. The complete question is:
On a coordinate plane, a line is drawn from point L to point M. Point L is at (negative 4, 8) and point M is at (4, 8). 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 ??.
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.
What is the dilation of a segment to its image?
The dilation of a segment to its image is the following of a given rule for every point on the segment to create an image.
How do we solve the given question?
We are given a line segment LM, with coordinates of L being (-4, 8) and that of M being (4, 8).
We are given a rule [tex]D_{O, 0.25} (x,y) \rightarrow (0.25x,0.25y)[/tex] which implies that every point on the line segment LM (x, y) is dilated to the point on the image L'M' as (0.25x, 0.25y).
The coordinates of L' in the image = (0.25*(-4), 0.25*8) = (-1, 2).
The coordinates of M' in the image = (0.25*(4), 0.25*8) = (1, 2).
The length of L'M' can be calculated using the distance formula between the points L' and M'.
Length = √((2 - 2)² + (1 - (-1))²) = √(0² + 2²) = √4 = 2 units.
∴ The length of L'M' = 2 units.
The slope of both LM and L'M' is 0, as they both are parallel to the x-axis and don't intersect with it.
∴ 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.
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