Reflect a Point Across y = x

Reflecting a Point Across (y=x)

Reflecting across the line (y=x) means the point is flipped over the diagonal line where the coordinates are equal. The key effect is simple:

• the (x)-coordinate and (y)-coordinate switch places.

Method

1. Start with the point ((x, y)).
2. Swap the coordinates to get ((y, x)).
3. Write the reflected point in simplified form.

Example pattern

• ((3, -5)) reflects to ((-5, 3))
• ((-2, 7)) reflects to ((7, -2))

Why this works

The line (y=x) is exactly the set of points where the two coordinates match. Reflecting across it exchanges horizontal and vertical position while keeping the same distance from the line.

Check your answer

A quick check is to make sure the original point and its image have reversed coordinates. If you swap them back, you should recover the original point. Also, if a point lies on (y=x), it stays in the same place after reflection.