Question

Given X (5, -8). What are the coordinates of X" if X" = Rx-axis

(Ry-axis(X))?

A. (5,8)
B. (-5,-8)
C. (-5,8)
D. (5,-8)

Answer 1

Answer: Choice C

(-5, 8)

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These are two rules to memorize

`\text{x-axis reflection: } \ \ (\text{x},\text{y})\to (\text{x},-\text{y})\\\\\text{y-axis reflection: } \ \ (\text{x},\text{y})\to (-\text{x},\text{y})\\\\`

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I'll relabel the point X as point A.

We apply a y-axis reflection first.

So we have:

`(\text{x},\text{y})\to (-\text{x},\text{y})\\\\(5,-8)\to (-5,-8)\\\\`

after the y axis reflection is applied.

This is the location of point A'

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Then we apply an x-axis reflection.

`(\text{x},\text{y})\to (\text{x},-\text{y})\\\\(-5,-8)\to (-5,-(-8))\\\\(-5,-8)\to \boldsymbol{(-5,8)}\\\\`

This is the location of point A''

which points us to choice C as the final answer.

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Side note:

The composition of an x-axis reflection and y-axis reflection, in either order, is the same as a 180 degree rotation around the origin.

The rule for a 180 degree rotation is
`(\text{x},\text{y})\to (-\text{x},-\text{y})\\\\`