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Question 5

Describe the reflection that maps ST, with vertices S(-7, 1) and T(-7, 5), onto itself. Use decimals, if necessary.
reflection in the line y =______

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Final answer:

The reflection that maps segment ST, with vertices S(-7, 1) and T(-7, 5), onto itself is a reflection in the horizontal line y = 3, which is the line that passes through the midpoint of the segment.

Step-by-step explanation:

The question involves understanding the concept of geometric reflections in the coordinate plane. To find the line of reflection that maps a segment onto itself, we observe the coordinates of the points defining the segment. Segment ST, with vertices S(-7, 1) and T(-7, 5), is vertical because both points have the same x-coordinate but different y-coordinates.

For a vertical segment to be reflected onto itself, the line of reflection must be a horizontal line that runs through the midpoint of the segment. The midpoint of segment ST is at the same x-coordinate, -7, and the average of the y-coordinates of S and T, which is (1+5)/2 = 3. Thus, the required line of reflection is the horizontal line y = 3.

The reflection that maps segment ST onto itself is, therefore, reflection in the line y = 3.

User Ayoub Boumzebra
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