The equation of the line of symmetry

To describe a reflection on a grid, the equation of the mirror line is needed.

Example

Reflect the shape in the line x = -1.

Triangle ABC on a set of co-ordinates

The line x = -1 is a vertical line which passes through -1 on the x-axis.

Triangle (ABC) reflected in the line, x=-1
Question

Describe the transformation of the shape ABC.

Triangle (ABC) reflected in the line, y=1

The line y = 1 is a horizontal line which passes through 1 on the y-axis.

The shape has been reflected in the line y = 1.

Question

Reflect the shape in the line y = x.

Triangle ABC on a set of co-ordinates

The equation of a straight line graph has the form y = mx + c, where m is the gradient and c is where the line crosses the y-axis.

The line y = x has a gradient of 1 and crosses the y-axis at (0,0).

Triangle (ABC) reflected in the line, y=x
Question

Describe the transformation of the shape ABC.

Triangle (ABC) reflected in the line, y=-x

The mirror line has a gradient of -1 and crosses the y-axis at (0,0).

The shape has been reflected in the line y = -x.

curriculum-key-fact
The equation of the mirror line is needed to fully describe a reflection.