9-1: Reflections.

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Presentation transcript:

9-1: Reflections

Definitions preimage-the shape before it is transformed. reflection-a transformation representing a flip of a figure. isometry-when the result of a transformation and its preimage are congruent. A reflection is an isometry.

You can reflect an image about a line or a point. The main reflections we will consider are: Lines Reflection over x-axis Reflection over y-axis Reflection over y=x Point – reflection over origin.

Reflect point A over the x-axis. What changes about the coordinates of the points?

Reflect point B over the y-axis. What changes about the coordinates of the points?

Reflect point C over the origin. What changes about the coordinates of the points?

Reflect point D over the line y=x. What changes about the coordinates of the points?

Reflection Preimage to image Example x-axis (a,b) →(a,-b) A=(3,2) A’=(3,-2) y-axis (a,b) →(-a,b) B=(4,5) B’=(-4,5) origin (a,b) →(-a,-b) C=(-2,-5) C’=(2,5) y=x (a,b) →(b,a) D=(4,7) D’=(7,4)

Reflect the point A(4,5) over the x-axis. Reflect the triangle with A(-2,1), B(3,4) and C(0,7) over the origin. Reflect the square with A(3,0), B(3,3), C(0,3) and D(0,0) over the line y=x.

Symmetry Line of symmetry – when you fold the shape over this line the two halves match exactly. EX: Point of symmetry – a point that is a common point of reflection for all points on a figure.

How to write coordinates as a matrix. The dimensions of your matrix will always be (2 x # of points) x-values go in the first row y-values go in the bottom row EX: Write a vertex matrix for quadrilateral ABCD with A(2,3) B(-4,5) C(-5,-2) D(0,-2)

Reflection matrices x-axis→ y-axis → origin → y=x →

Use the reflection matrices to reflect the pentagon with the following vertex matrix over the… 1. x-axis 2. y-axis

Reflect the following shape about the line y=x.

Assignment WB 9-1 Worksheet 9-1