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Master Enlargement and Reduction Scale Factors in Geometry

MA.912.GR.1.1

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

MA.912.GR.1.2

Classifying triangles

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

MA.912.GR.1.3

Isosceles and equilateral triangles

MA.912.GR.1.6

Similar triangles

Similar polygons

MA.912.GR.2.1

Rotational symmetry and transformations

MA.912.GR.2.2

Enlargements and reductions with scale factors

MA.912.GR.2.3

Scale diagrams

MA.912.GR.2.5

Introduction to transformations

Horizontal and vertical distances

MA.912.GR.2.6

Draw on coordinate planes

MA.912.GR.2.8

Cartesian plane

Cartesian Plane — Coordinates

MA.912.GR.3.1

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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>

MA.912.GR.3.2

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

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>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

MA.912.GR.3.3

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

MA.912.GR.4.1

Surface area of 3-dimensional shapes

MA.912.GR.4.2

Line symmetry

MA.912.GR.4.3

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

MA.912.GR.4.5

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

MA.912.GR.4.6

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

MA.912.GR.5.1

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

MA.912.GR.5.2

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

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

MA.912.GR.5.3

Circles and circumference

Circle properties

MA.912.GR.6.1

Arcs of a circle

MA.912.GR.6.2

Areas and sectors of circles

Central angles and proofs

Inscribed angles and proofs

MA.912.GR.6.3

Central and inscribed angles in circles

Circle chord, tangent, and inscribed angles proofs

MA.912.GR.6.4

Angles in a circle

Chord properties

Tangent properties

MA.912.GR.7.2

Conics - Circle

MA.912.GR.7.3

Conics - Parabola

Conics - Ellipse

Conics - Hyperbola

MA.912.LT.4.10

Biconditionals

Deductive reasoning

Algebraic proofs

MA.912.LT.4.3

Inductive reasoning

Statements

Negations

Conjunctions and disjunctions

Truth tables

Conditionals

Inverses, converses, and contrapositives

MA.912.T.1.1

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

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Use tangent ratio to calculate angles and sides (Tan = o / a)

MA.912.T.1.2

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

math

Intro

<p>- Hi, welcome to this question right here. So, we're trying to redraw this shape right here, using a scale factor of one-quarter. So, it's gonna get smaller. But, how much smaller? About a quarter smaller, right?<br />
So, what we're gonna do is, we're gonna figure out the, I guess, how many units you have on the original part first, right? So, if I count it on the middle line right there, that's about 8 boxes in total. And the high here is just gonna be 2 boxes here, and 2 boxes here. And from here to here, it's just going to be 1, 2, 3, 4, looks like a 5, okay?<br />
Now, we're gonna take this whole...every dimension here and we're gonna divide by 4. So, let's look at the center line first, because it's easier. 8 divided by 4, what do we have? We've got 2. So it's gonna be very small. So I come over to the center line right here. I'm gonna draw a center line and that's gonna be a new shape right there. If I divide this 8 by 4, right? So, I've got 2 right now. Now, it's gonna go from the center down to this one before. Remember, you're multiplying by a quarter, which means you're dividing by four. So, what's 2 divided by 4? It's gonna be a one-half and one-half is 0.5. So from the center line I'm gonna go down 0.5 so, about here I'm gonna stop. Go up 0.5 and I'm going to stop. Because I've got to figure out how much is, how long is here and how long is here. Well, this is 5. From the center of the figure here, this is 5 so, if I take this 5 here and divide by 4, I've got 1.25. And it's like this, a 1.25 is the total length. From here to here is 1.25 so, it's a little bit approximate. It doesn't have to be very exact. So, here's my 1.25. Here's my little 1.25 right there. Let me redraw it a little bit. So, 1.25. So at the end we're just gonna put everything together. And there you go. That is your new drawing. If you times it by a one-quarter? Kind of look small but, there's nothing else we can do. Divide everything by 4, that's what you get. Thanks for watching.</p>


When you are asked to make an object bigger or smaller, you will ask, "by how much?" In this case, scale factor can help answer the question. In this lesson, we will practice how to enlarge and reduce objects according to the scale factors given to us.

What is a scale factor?

Ratios

Rates

Proportions