Reflections

Reflections of shapes on a coordinate grid involve flipping the shape over a mirror line to create a mirror image. One way to ensure accuracy when reflecting shapes is to measure the number of squares between each vertex (corner) and the mirror line.

Reflection of a Shape Over the x-Axis

To reflect a shape over the x-axis, measure the number of squares between each point on the shape and the x-axis. If a point is 3 squares above the x-axis, its reflection will be 3 squares below the x-axis.

For example, if a triangle has vertices at \( (2, 3) \), \( (4, 1) \), and \( (5, 4) \), reflecting the shape over the x-axis would result in new vertices at \( (2, -3) \), \( (4, -1) \), and \( (5, -4) \).

Reflection of a Shape Over the y-Axis

To reflect a shape over the y-axis, measure the number of squares between each point on the shape and the y-axis.

For example, if a point is 4 squares to the right of the y-axis, its reflection will be 4 squares to the left. If a triangle has vertices at \( (2, 3) \), \( (4, 1) \), and \( (5, 4) \), reflecting over the y-axis would give the new vertices at \( (-2, 3) \), \( (-4, 1) \), and \( (-5, 4) \).

Reflection of a Shape Over the Line \( y = x \)

To reflect a shape over the line \( y = x \), measure how far each point is from the line, in terms of diagonal squares.

Describing a Reflection

When describing a reflection, you will need to state that the transformation is a reflection, and you will need to describe the mirror line (x-axis, y-axis, or any other line such as \( y = x \)).