About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Mastering Rotational Symmetry and Transformations in Geometry

Derive proofs that involve the properties of angles and triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems that involve the properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Solve problems that involve the cosine law and the sine law including the ambiguous case

auto-gen

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Analyze and prove conjectures using inductive and deductive reasoning to solve problems

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Analyze puzzles and games that involve spatial reasoning using problem-solving strategies

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Arithmetic mean vs. Geometric mean

Solve problems that involve the application of rates

Applications of rational equations

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Solve problems that involve scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Simplifying complex fractions

Demonstrate understanding of relationships among scale factors areas surface areas and volumes

Quadratic function in vertex form: y = a(x-p)^2 + q

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Model and solve problems that involve systems of linear inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of quadratic functions

Introduction to quadratic functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Completing the square

Completing the Square

Research and give a presentation on a historical event or area of interest that involves mathematics

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Demonstrate understanding of normal distribution including standard deviation and z-scores

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Interpret statistical data using confidence intervals confidence levels and margin of error

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Grade 11 Applied Mathematics (30S)

Develop spatial sense

Develop logical reasoning

Develop spatial sense and proportional reasoning

Develop algebraic and graphical reasoning through the study of relations

Develop an appreciation of the role of mathematics in society

Develop statistical reasoning

math

Intro

Ex. 1:

Ex. 2:

<p>- Hi, welcome to this question right here. So here we are. This figure right here, it says in the question it does have a rotation symmetry. So the first part of the question asks you, "Where is the center of rotation?" Now, all you have to do is just pick the center of your image and they have to know that this point, if you rotate it, it will form exactly the same image after you rotate it to certain degrees. So for this figure right here is a rectangular shape, the green part, right? So the center of the symmetry, or I'd say the center of rotation will be this point right here. So you can imagine that if you have a piece of paper with this size and if you rotate that piece of paper around, you will still get the same image, okay? So what are the order and the angle of rotation? The order of the rotation is this. You can actually relate the order to the line of symmetry you have. So if you look at the square right here, you have four symmetrical lines. You got one this way, this way, and this way, and then this way. So there's four lines. So technically the order of rotation for this question will be a four, okay? Now, the angle of rotation, you can actually calculate it. It's pretty simple. You see, when we rotate things around, it's actually 360. So to calculate this, it's 360 and all you have to do is divide it by the order number that you found, which is four. Now once again, to figure the order, all you have to do is figure a line of symmetry you have. So let's just quickly draw that. So we&apos;ve got one line going down this way. This is one symmetrical line and this is two and this is three and this is four. So with four lines of symmetry, you can actually relate that to the order number. So to calculate the angle of rotation, just take the 360, which is one complete turn, it's always 360 by the way, and divide it by four, the orders that you have. Now 360 divided by four, using your calculator, you get yourself a 90 degrees. So that's your angle of rotation right there, 90 degrees. It says, "Show your answers in degrees," which is this one right here and/or as a fraction of a turn. Now, a fraction of a turn, it's 360, right? So if you take that and divide it by 360, which is 90 divided by 360 again, basically you get yourself a one quarter, and this is your one quarter of a turn for this question. That's it. Thanks for watching.</p>


When an object is turned around its center of rotation to certain <a href='[[glossary.html|{"keyword":"Degree","term":"Degree"}]]'>degrees</a> and the object looks the same, we can say it has rotational symmetry. We will learn the details of rotational symmetry including, lines of symmetry, order of rotation, and angle of rotation.   