Unit 3 Review

​Algebraic form: T_h,k(x,y)➜(x+h, y+k)

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​To perform a translation, add the h value to the x value of your point (If h is negative subtract it), then add the k value to the y value of your point (If k is negative subtract it).

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​Remember:

Horizontally (h) right is positive and left is negative

​Vertically (k) up is positive and down is negative.

​Remember our four rules for reflections:

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• ​r_x-axis(x, y) ➜ (x, -y)

• ​​r_y-axis(x, y) ➜ (-x, y)

• ​​r_y=x(x, y) ➜ (y, x)

• ​​r_y=-x(x, y) ➜ (-y, -x)

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​Our rotation rules: ➜ °

​Counter clockwise(positive):

• R_90°(x, y)➜(-y, x)

• ​R_180°(x, y)➜(-x, -y)

• ​R_270°(x, y)➜(y, -x)

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​Clockwise (Negative):

• ​R_-90°(x, y)➜(y, -x)

• ​R_-180°(x, y)➜(-x, -y)

• ​R_-270°(x, y)➜(-y, x)

​Two kinds of symmetry:

• ​Line Symmetry: Reflection that maps a figure to itself.

• ​Rotational Symmetry: Rotation that maps a figure to itself.

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​Smallest possible angle of rotational symmetry: 360/n

​(n is the number of sides of the polygon)

​Remember to test if smallest possible angle works. Keep testing all multiples of smallest possible angle until reaching 180 degrees.

​Remember:

​Parallel slopes are equal

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​Perpendicular slopes are opposite reciprocals (Flip-Change).

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​Steps to find line:

1. ​Find slope m

2. ​Plug into y = mx+b with given point (x, y) to solve for b

3. ​Plug m and b into y = mx +b