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Master Shape Transformations with Matrices | Math Guide

NY.A-APR.C.5+

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Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

Determining the equation of a polynomial function

NY.A-APR.D.7+

Descartes&apos; rule of signs

Descartes' Rule of Signs

Descartes' rule of signs

Descartes" rule of signs

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Negative exponent rule

NY.F-BF.B.5+

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Solving exponential equations with logarithms

Product rule of logarithms

NY.F-TF.A.3+

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Find the exact value of trigonometric ratios

NY.F-TF.C.8+

Pythagorean identities

NY.F-TF.C.9+

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

NY.G-SRT.D.10+

Law of sines

Ambiguous case: SSA triangles

Law of cosines

NY.G-SRT.D.11+

Applications of the sine law and cosine law

NY.G-SRT.D.9+

Area of triangles: 1/2 a*b sin(C)

NY.N-CN.A.3+

Complex conjugates

Complex Conjugates

Distance and midpoint of complex numbers

Angle and absolute value of complex numbers

NY.N-CN.B.4+

Polar form of complex numbers

NY.N-CN.B.5+

Operations on complex numbers in polar form

NY.N-CN.B.6+

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

NY.N-CN.C.8+

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Solving polynomials with unknown coefficients

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

NY.N-CN.C.9+

Word problems of polynomials

Fundamental theorem of algebra

NY.N-VM.A.1+

Use sine ratio to calculate angles and sides (Sin = o / h)

Introduction to vectors

Magnitude of a vector

Direction angle of a vector

NY.N-VM.A.2+

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Scalar multiplication of vectors

Equivalent vectors

NY.N-VM.A.3+

Word problems on vectors

Word problems relating guy wire in trigonometry

NY.N-VM.B.4+

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

NY.N-VM.B.5+

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

Unit vector

NY.N-VM.C.10+

Zero matrix

Identity matrix

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The Inverse of a 2 x 2 matrix

NY.N-VM.C.11+

Transforming vectors with matrices

Transforming shapes with matrices

NY.N-VM.C.12+

Finding the transformation matrix

NY.N-VM.C.6+

Notation of matrices

Adding and subtracting matrices

NY.N-VM.C.7+

Scalar multiplication of matrices

NY.N-VM.C.8+

Matrix multiplication

The three types of matrix row operations

NY.N-VM.C.9+

Properties of matrix multiplication

Plus (+) Standards

math

Intro

Ex.1

Ex.2

Ex.3

Ex.4

In this section, we will learn how to transform shapes with matrices. Instead of one column vector, we are going to have multiple vertices which create a shape. What we can do to this shape is use the transformation matrix to change the length and size of that shape. To do this computation, we merge all the vertices into one matrix and then multiply it with the transformation matrix. Doing so will give us another matrix. We will then take a look at each transformed vertices separately in the matrix to see the new transformed shape. Note that transforming the shape does not change the number of sides. We will take a look at some questions which involve transforming shapes, and then graph them to notice the changes between the normal shape and the transformed shape.

Multiplying a matrix by another matrix