Assume that p is a relation that contains the points (3, -4). What other point must be included in the relation if p is:1. symmetric about the x-axis?2. symmetric about the y-axis?

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23-09-2021
Mathematics

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Assume that p is a relation that contains the points (3, -4). What other point must be included in the relation if p is:1. symmetric about the x-axis?2. symmetric about the y-axis?

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xero099 xero099 · Answer 1 · 2021-10-03T16:35:05+02:00

The point needed for the relation is [tex]P(x,y) = (3, 4)[/tex] if P and P' are symmetric about the x-axis.

The point needed for the relation is [tex]P(x,y) = (-3, -4)[/tex] if P and P' are symmetric about the y-axis.

In this exercise we are supposed to determine the coordinates of a point P under an assumption of rigid transformation. Now, we must use the following symmetry transformations:

Reflection about the x-axis

[tex]S'(x,y) = S(x,y) - 2\cdot (0, s_{y})[/tex] (1)

Reflection about the y-axis

[tex]S'(x,y) = S(x,y) - 2\cdot (s_{x}, 0)[/tex] (2)

Where:

[tex]S(x,y)[/tex] - Original point.
[tex]S' (x,y)[/tex] - Reflected point.
[tex]s_{x}, s_{y}[/tex] - Coordinates of point S.

If we know that [tex]P'(x,y) = (3, -4)[/tex], the coordinates for each reflection are, respectively:

Reflection about the x-axis

[tex]P(x,y) = (3,-4) - 2\cdot (0, -4)[/tex]

[tex]P(x,y) = (3, 4)[/tex]

[tex]P(x,y) = (3, 4)[/tex] if P and P' are symmetric about the x-axis.

Reflection about the y-axis

[tex]P(x,y) = (3, -4) - 2\cdot (3, 0)[/tex]

[tex]P(x,y) = (-3, -4)[/tex]

[tex]P(x,y) = (-3, -4)[/tex] if P and P' are symmetric about the y-axis.

We kindly invite to see this question on rigid transformations: https://brainly.com/question/18613109