Transformations: ◦ Translation: slide ◦ Rotation: turn ◦ Reflection: flip/mirror image ◦...
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Transcript of Transformations: ◦ Translation: slide ◦ Rotation: turn ◦ Reflection: flip/mirror image ◦...
Transformations:◦ Translation:
slide◦ Rotation:
turn◦ Reflection:
flip/mirror image◦ Dilation:
enlarge / reduce
Types of Transformations
Rules:◦ Rotation
90 around the origin (x, y) -> (y, -x)
180 around the origin (x, y) -> (-x, -y)
270 around the origin(x, y) -> (-y, x)
◦ Reflection Over the x- axis (x, y) ->
(x, -y) Over the y-axis (x, y) ->
(-x, y)
◦ Translation (x, y) -> Up/down add to the Y Left/Right add to the X
◦ Dilation (x, y) -> Multiple to both the x and y
Transformation
Congruent◦ Same Shape, Same Angles, Same Size
Similar◦ Same Shape, Same Angles, DIFFERENT Size
Congruent VS Similar
Opposite / Vertical angles:◦ When 2 angles intersect; share a vertex
Corresponding angles:◦ Same position; same side of transversal
Alternate exterior angles: ◦ Outside of parallel lines, opposite side of transversal
Alternate interior angles: ◦ Inside of parallel lines, opposite side of transversal
Supplementary angles: ◦ Angles that form a straight line
Complementary angles: ◦ Angles that form a right angle
Angles
Anglesa)Opposite / Vertical angles
b)Corresponding angles
c) Alternate exterior angles
d)Alternate interior angles
e)Supplementary angles
f) Complementary angles
Negative Exponents – rewrite as a fraction ex: =
Any base raised to the zero power has a value of 1
Exponents
Very LARGE numbers will have a POSITIVE exponent
Very SMALL numbers will have a NEGATIVE exponent
Scientific Notation
Write in decimal notation: 3.6 × 108
Convert 4.2 × 10–7 to decimal notation.
Convert 93,000,000 to scientific notation.
Scientific Notation
Simplify and express in scientific notation: (2.6 × 105) (9.2 × 10–13)
Simplify and express in scientific notation: (8.2 × 10–3) ÷ (4 × 10–2)
Scientific Notation
Rational #s= fractions, repeating decimals, terminating decimals, whole numbers, perfect square roots
Irrational #s= non-terminating and non-repeating decimals, non-perfect squares, and pi
Rational and Irrational #s
http://www.math-play.com/rational-and-irrational-numbers-game/rational-and-irrational-numbers-game.html
Non-perfect square roots Find the perfect squares that are closest to
the number. Estimate a value between the square roots
of the two closest perfect squares. EX:
Square Roots
http://www.crctlessons.com/Slope-Intercept-Test/slope-intercept-test.html
Linear Equations
To find the x-intercept, set y = 0 To find the y-intercept, set x=0
Example find the x and y-intercepts:3x + 4y = 12
X and Y Intercepts
http://www.crctlessons.com/Pythagorean-theorem-game.html
Pythagorean Theorem
Cylinder= πr2h
Cone=1⁄3πr2h
Sphere= 4⁄3πr3
http://www.flocabulary.com/volume-cone-cylinder-sphere/
Volume
Big B = Area of the b
b= base
EX: Volume of a Cone V=1/3Bh◦ What does the “B” stand for?
Big B / Little b
Any function that forms a straight line Has a constant rate of change Can be written in slope intercept form No exponents Does not have a variable in the
denominator Linear or nonlinear?? y = 3x y = + 8 y = - 7
Linear Functions
Tables:◦ The x value cannot repeat
Ordered Pairs◦ The x value cannot repeat
Graphs:◦ Vertical Line Test – only touches in 1 spot
Functions