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Find a formula for the transformation of reflection across the line l with equation y = -x.

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Answer:

The rule or formula for the transformation of reflection across the line l with equation y = -x will be:

P(x, y) ⇒ P'(-y, -x)

Explanation:

Considering the point


P(x, y)

If we reflect a point
P(x, y) across the line
l with equation
y = -x, the coordinates of the point P flips their places and the sign of the coordinates reverses.

Thus, the rule or formula for the transformation of reflection across the line l with equation y = -x will be:

P(x, y) ⇒ P'(-y, -x)

For example, if we reflect a point, let suppose A(1, 3), across the line
l with equation
y = -x, the coordinates of point A flips their places and the sign of the coordinates reverses.

Hence,

A(1, 3) ⇒ A'(-3, -1)

User Frank Martin
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