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In the lesson, you used the following matrices to create reflections:

Across x-axis: A =
[1 0]
[0 −1]

Across y-axis: B =
[-1 0]
[0 1]

Across line y = x: C =
[0 1]
[1 0]

Across line y = −x: D =
[0 -1]
[-1 0]

All these reflections resulted in ________ figures.

User Thanassis
by
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2 Answers

6 votes

Final answer:

The reflections created by matrices A, B, C, and D result in congruent figures, which are identical in shape and size, but mirrored across the respective axis or line.

Step-by-step explanation:

When matrices A, B, C, and D are used to create reflections of geometric figures across various lines, the resulting figures are identical in shape and size to the original figures, but are flipped or mirrored with respect to the line of reflection. For instance, the reflection across the x-axis using matrix A involves flipping the figure over the x-axis, such that points above the x-axis are mapped to an equal distance below it, and vice versa. Similarly, reflections across the y-axis, the line y = x, and the line y = -x, using matrices B, C, and D, respectively, result in similar operations where the figure is flipped across the corresponding line. Each of these operations preserves the sizes and angles of the shapes; thus, the reflected figures are considered congruent to the original figures.

User Akuzminykh
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Answer:

All these reflections resulted in ________ figures.

Answer: Congruent

Find the determinant of each of these:

The determinant of each of these is ___.

Answer: -1

Now find the following:

A=1 B= 0 C=0 D=1

Repeat this process for the other three matrices. The product of a reflection matrix and its transpose is the ___________.

Answer: Identity Matrix

Step-by-step explanation:

I took the quiz on edge.

User Dennis Kieselhorst
by
2.9k points