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 $y=x$).