10/25/16- Intro to Reflections

Warm-Up

a. Plot three coordinates whose x-values equal -2.

b. Plot three coordinates whose y-values equal 4.

c. Plot three coordinates whose x-values and y-values are equal.

d. Plot three coordinates whose x-values and y-values are opposites.

We then connected the lines of each of the above example, and concluded:

For (a) all of the points on that line have an x-value of -2, so the equation of the line is x=-2.

For (b) all of the points on that line have an y-value of 4, so the equation of the line is y=4.

For (c) all of the points on that line have equal x and y values, so the equation of the line is y = x.

For (d) all of the points on that line have opposite x and y values, so the equation of the line is y = -x.

Key Idea: To create a graph of a line from its equation, plot points that meet the conditions of the equation (Ex: If x=-2, create points with an x-value of -2).

Reflections (Flip)

Rigid motion, described using a line of reflection.

Key Idea: The line of reflection is the perpendicular bisector of the segments connecting a pre-image point to its image.

See picture example accompanying notes below:


Reflections on the Coordinate Plane

(We used a small piece of 10×10 graph paper to visualize the effect of different reflections on the coordinate plane, by folding it along each line of reflection and seeing where the point (3, 4) ended up. We then used that pattern to give another example of where (-2,-3) would be mapped to, and finally what (x,y) would generally be mapped to.)

Reflection across the x-axis

Ex.) (3, 4)–>(3, -4); (-2, -3)–> (-2, 3); (x, y)–> (x, -y)

Reflection across the y-axis

Ex.) (3, 4)–>(-3, 4); (-2, -3)–> (2, -3); (x, y)–> (-x, y)

Reflection across y=x

Ex.) (3, 4)–>(4, 3); (-2, -3)–> (-3, -2); (x, y)–> (y, x)

Reflection across y=-x

Ex.) (3, 4)–>(-4, -3); (-2, -3)–> (3, 2); (x, y)–> (-y, -x)

We then completed p. 112- 113: 1-5.

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