Answer:
The original point is [tex]P(x,y) = (3,9)[/tex].
The distance between the points is 18 units.
Step-by-step explanation:
The reflection of a point with respect to the x-axis is defined by the following operation:
[tex]P(x,y) = (x,y) \to P'(x,y) = (x, -y)[/tex] (1)
Where:
[tex]P(x,y)[/tex] - Original point.
[tex]P'(x,y)[/tex] - Resulting point.
If we know that [tex]P'(x,y) = (3, -9)[/tex], then the original point is [tex]P(x,y) = (3,9)[/tex].
The original point is [tex]P(x,y) = (3,9)[/tex].
The distance between the points ([tex]d[/tex]), in units, is determined vectorially by the following expression, which is equivalent to the Pythagorean Theorem:
[tex]d = \sqrt{[P'(x,y) -P(x,y)]\,\bullet\,[P'(x,y) -P(x,y)]}[/tex]
[tex]d = \sqrt{(0,18)\,\bullet (0,18)}[/tex]
[tex]d = \sqrt{0^{2}+18^{2}}[/tex]
[tex]d = 18[/tex]
The distance between the points is 18 units.
