Step by step
The question
Question: reflect the point P(1, 4) in the line y = x.
1 Draw the shape
Put the point on the grid.
2 Draw the mirror line
The mirror line is the line y = x.
It goes through (0, 0), (1, 1), (2, 2) and so on.
Reflecting flips the shape over the line, like a mirror.
Each point lands just as far away, on the other side.
3 Reflect each point
From P, go straight to the mirror line, at a right angle to it.
Then go the same again, past the line.
We call the new point P prime.
The little mark means: the new P.
P is (1, 4).
Across the mirror line, P' is (4, 1).
Careful!
Over the line y = x, the two numbers swap places.
Their signs do not change.
4 The new point
So the image is P'(4, 1).
5 Check
Let's check with the rule for the line y = x: x and y swap places.
It gives the same points.
Right!
Let's look back.
First: draw the shape.
Then: draw the mirror line.
Then: reflect each point.
Then: the new point.
Last: check.