Reflections. What will we accomplish in today’s lesson? Given a pre-image and its reflected image, determine the line of reflection. Given a pre-image.

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Presentation transcript:

Reflections

What will we accomplish in today’s lesson? Given a pre-image and its reflected image, determine the line of reflection. Given a pre-image and its reflected image graphed on the coordinate plane, determine the line of reflection and give a function rule for the reflection. Given the line of reflection, draw a reflection on plain paper. Given a horizontal or vertical line of reflection or function rule, draw a reflection on the coordinate plane. Reflections A reflection is a transformation that flips a figure across a line, called the line of reflection. Segments connecting corresponding points of a pre-image and its reflected image are bisected by the line of reflection. Corresponding points of a pre-image and its reflected image are equidistant from the line of reflection. The reflection of a figure changes orientation so that it faces in the opposite direction of the original figure.

What is a reflection? A reflection is a transformation that flips a figure over a line called the line of reflection. A reflection is a type of rigid transformation. line of reflection (the x-axis in this example)

Properties of Reflections Segments connecting corresponding points of a pre-image and its reflected image are bisected by the line of reflection.

Properties of Reflections Corresponding points of a pre-image and its reflected image are equidistant from the line of reflection. The reflection of a figure changes orientation so that it faces in the opposite direction of the original figure.

Coordinate notation for reflections in the coordinate plane 3 rules for reflections in a coordinate plane reflection across the x-axis: (x, y)  (x, -y) reflection across the y-axis: (x, y)  (-x, y) reflection across the line y=x: (x, y)  (y, x)

Reflect the following figure across the x-axis pre-image points (1,1) (4,1) (4,4)

Reflect the following figure across the y-axis

Reflect the following figure across the line y=x pre-image points (-3,2) (-1,2) (-1,5)

Options for the line of reflection A reflection can occur across any line. It is not limited just to the x-axis, y-axis, and line y=x.

Identifying the equation for the line of reflection helps to see the change between the coordinates of the pre-image and image. The line of reflection is represented by the equation x = -2. To begin, find the distance from the pre-image point to the line of reflection. Each image point must be that same distance in the opposite direction from the line of reflection. For example, point A is 3 units from the line of reflection. So A' must be three units in the opposite direction from the line of reflection.

Reflect the figure across the line x=2 pre-image points (1,4) (1,1) (0,1)

Reflect the line across y=3 pre-image points (7,3) (-1,7) (1,4) (6,3)

Try it yourself! ties/Transmographer/