Answer:
The segment connecting two corresponding points on the image and pre-image is a perpendicular bisector, so the line of reflection bisects the segment and the segment is perpendicular to the line of reflection, or intersects the line at a 90 degree angle. ... A transformation in which the image and pre-image are congruent.
The translation moves each point on the pre-image the same distance
horizontally and vertically to location of the image.
The completed paragraph is; When I use line segments to connect the
corresponding points of a pre-image and the image in a translation, the line
segments are parallel, because, their slope (ratio of Rise to Run) are equal.
Reasons:
Connecting the corresponding points of a pre-image and the formed
image in a translation transformation with line segments give lines that are
parallel to each other, given that the Rise (change in the y-value) and Run
(change in the x-values) are equal.
The translation between two points are [tex]\mathbf{T_{(\Delta x, \ \Delta y)}}[/tex]
[tex]\mathrm{The \ slope \ between \ the \ points \ is} \ \dfrac{\Delta y}{\Delta x}[/tex]
Therefore, the connecting lines have the same slope and are therefore,
parallel.
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