Question

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

Answer 1

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)