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A dilation stretches or shrinks a figure by a scale factor relative to a fixed center point. The scale factor is the ratio of the length of a side of the image to the corresponding side of the original figure. A scale factor greater than 1 results in an enlargement, while a scale factor between 0 and 1 results in a reduction. Under coordinate notation, a dilation transforms each point (x,y) to (kx, ky) where k is the scale factor. Diagrams show that for a dilation centered at the origin, the point and its image always lie on the same ray from the origin.
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6.7 notes
6.7 notesMrs. Hedrick's Class
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The document discusses dilations, which are transformations that stretch or shrink shapes by a scale factor relative to a fixed center point. A dilation is notated as (x,y) -> (kx, ky), where k is the scale factor and (x,y) are the original coordinates being dilated. If k is between 0 and 1, it represents a reduction, while if k is greater than 1, it represents an enlargement. Points on a figure and their images under a dilation lie on the same ray from the center of dilation.Billboard - Austin
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Part of a statewide expansion campaign designed to build brand recognition before actual product launch.Trig 1 notes
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3.6 notesMrs. Hedrick's Class
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This document discusses several theorems about perpendicular lines:
- If two lines intersect to form congruent angles, then the lines are perpendicular.
- If two lines are perpendicular, then they intersect to form four right angles.
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- If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
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This document appears to be notes from a class or homework on finance charge methods for credit cards and loans. It includes examples of calculating average daily balances, finance charges, and new balances using different balance calculation methods (previous balance method, adjusted balance method, average daily balance method). It also includes practice problems for students to calculate average daily balances, finance charges, and new balances given transaction histories for a sample credit card.2.3 notes
2.3 notesMrs. Hedrick's Class
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10.4 notesMrs. Hedrick's Class
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The document discusses inscribed angles and polygons:
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12.3 notesMrs. Hedrick's Class
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1) The document provides instructions to find the surface area of various 3D shapes including dodecahedrons, icosahedrons, regular pyramids, and cones.
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3) The bellwork is to be turned into the homework bin.6.7 notes
6.7 notesMrs. Hedrick's Class
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The document discusses the concept of dilation in geometry. Dilation stretches or shrinks a figure by a scale factor relative to a fixed center point. Dilation can enlarge or reduce a figure depending on whether the scale factor is greater than or less than 1, respectively. Examples of dilation are represented using coordinate notation and diagrams showing how points and their images are related by rays from the center of dilation. Homework problems on dilation are assigned from page 412, problems 3 through 21 of an odd-numbered variety.6.7 notes
6.7 notesMrs. Hedrick's Class
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The document discusses the concept of dilation in geometry. Dilation stretches or shrinks a figure by a scale factor relative to a fixed center point. If the scale factor is between 0 and 1, it is a reduction, while a scale factor greater than 1 results in an enlargement. Dilation can be expressed using coordinate notation where the x- and y-coordinates of points are each multiplied by the scale factor k.4.8 notes
4.8 notesMrs. Hedrick's Class
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9.7 notesMrs. Hedrick's Class
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The document discusses dilations in geometry. It defines dilations as reductions where the scale factor k is between 0 and 1, or enlargements where k is greater than 1. Dilations can be performed by multiplying the coordinates of a figure by a scalar value k. Matrices can also be used to represent dilations, with the scale factor k multiplied by the matrix of the original polygon. The document provides examples of dilation problems and assigns homework problems related to dilations.5.8 notes
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This document contains notes on laws of exponents from a math class. It discusses multiplying powers with the same base by adding the exponents, and raising a power to a power by multiplying the exponents. Students are assigned homework problems on simplifying expressions using these laws from page 207, numbers 2 through 36, and 42 through 44.Strafford Volleyball Apparel
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12.7 notesMrs. Hedrick's Class
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This document contains notes from a math class on similar solids. It defines similar solids as two solids of the same type that have equal ratios, known as a scale factor. It then states the Similar Solids Theorem: if two similar solids have a scale factor of a:b, their corresponding areas have a ratio of a2:b2 and their corresponding volumes have a ratio of a3:b3. Examples of homework problems involving similar solids are listed.12.6 notes
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The document discusses surface area and volume formulas for spheres. It provides examples of calculating the surface area of spheres with given diameters, as well as the volume of spheres and other objects like snow cones that can be modeled as spheres. Students are assigned homework problems applying these formulas to calculate surface areas and volumes.12.5 notes
12.5 notesMrs. Hedrick's Class
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The document is notes from a math class lesson on finding the volumes of cones and pyramids. It includes the objectives of learning the formulas for these volumes. The formulas given are that the volume of a cone is 1/3r^2h and the volume of a pyramid is 1/3Bh, where B is the area of the base and h is the height. There are examples provided of applying these formulas to find volumes.12.4 notes
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The document discusses surface area formulas for prisms and cylinders. It defines surface area as the sum of the areas of all surfaces that enclose a solid. For prisms, surface area is calculated as the perimeter of the base multiplied by the height, plus twice the area of the base. For cylinders, surface area is the circumference of the base multiplied by the height, plus twice the area of the circular base. The document provides examples of applying these formulas to prisms and cylinders.More Related Content
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6.7 notes
- 1. 6.7油Dilations November油22,油2011 13.5 12 23.8 Bellwork HW油pg.油412油#3足21油odds 1
- 2. 6.7油Dilations November油22,油2011 6.7 Similarity Transformations Dilation: stretches or shrinks Center of Dilation: fixed point Scale Factor: ratio of a side length to corresponding side length of original Coordinate Notation for a Dilation: (x,y) > (kx, ky) Reduction: 0 < k < 1 Enlargement: k > 1 HW油pg.油412油#3足21油odds 2
- 3. 6.7油Dilations November油22,油2011 HW油pg.油412油#3足21油odds 3
- 4. 6.7油Dilations November油22,油2011 HW油pg.油412油#3足21油odds 4
- 5. 6.7油Dilations November油22,油2011 Reading Diagrams A point of the figure and its image lie on the same ray from the origin for a center of dilation at the origin. HW油pg.油412油#3足21油odds 5
- 6. 6.7油Dilations November油22,油2011 HW pg. 412 #321 odds HW油pg.油412油#3足21油odds 6