Question

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?

Answer 1

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

The point needed for the relation is $P(x,y) = (-3, -4)$ 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

$S'(x,y) = S(x,y) - 2\cdot (0, s_{y})$ (1)

Reflection about the y-axis

$S'(x,y) = S(x,y) - 2\cdot (s_{x}, 0)$ (2)

Where:

• $S(x,y)$ - Original point.
• $S' (x,y)$ - Reflected point.
• $s_{x}, s_{y}$ - Coordinates of point S.

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

Reflection about the x-axis

$P(x,y) = (3,-4) - 2\cdot (0, -4)$

$P(x,y) = (3, 4)$

$P(x,y) = (3, 4)$ if P and P' are symmetric about the x-axis.

Reflection about the y-axis

$P(x,y) = (3, -4) - 2\cdot (3, 0)$

$P(x,y) = (-3, -4)$

$P(x,y) = (-3, -4)$ if P and P' are symmetric about the y-axis.

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