3.4.3 Journal: Transformations Journal Geometry Sem 2 (S2667506) Brian Galvan Points possible: 20 Date: ____________ Scenario: Miniature Golf Transformations Instructions: View the video found on page 1 of this journal activity. Using the information provided in the video‚ answer the questions below. Show your work for all calculations The Students’ Conjectures: The students have instructions about moving buildings on a miniature golf course. They disagree about the transformation involved
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Geometry Unit 1 Lesson 7 Assessment Column A (choose two of the following) Column B (choose one of the following) Construct a line segment and copy it. Construct an angle and copy it. Construct a line segment and bisect it. Construct an angle and bisect it. Construct parallel lines. Construct a perpendicular line through a point on the given line. Construct a perpendicular line through a point not on the given line. Construct an equilateral triangle inscribed in a circle. Construct a square
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segment PQ: In Euclidean geometry the perpendicular distance between the rays remains equal to the distance from P to Q as we move to the right. However‚ in the early nineteenth century two alternative geometries were proposed. In hyperbolic geometry (from the Greek hyperballein‚ "to exceed") the distance between the rays increases. In elliptic geometry (from the Greek elleipein‚ "to fall short") the distance decreases and the rays eventually meet. These non-Euclidean geometries were later incorporated
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EUCLID: The Man Who Created a Math Class Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create "The Elements" which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included‚ many of Eudoxus’ theorems‚ he perfected many of Theaetetus’s
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Coordinate geometry The Basics: Find the distance between two points using Pythagoras’ theorem. The midpoint is the average (mean) of the coordinates. The gradient = Parallel lines have the same gradient. The gradients of perpendicular lines have a product of -1. Straight Lines: Equation of a straight line is y = mx + c‚ where m = gradient‚ c = y-intercept. The equation of a line‚ if we know one point and the gradient is found using: (y - y1) = m(x - x1) (If given two points‚ find the
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Module one- Lesson 01.01 The terms point‚ line‚ and plane are referred to as undefined. When you write the definition of these terms‚ you have to rely on other terms that need defining. Point- In general‚ a point is a location. Because points have no size‚ you can say they have no dimension. Line- a "stream" of points that has no width or depth. You can also think of a line as points lined up next to each other that go on forever in opposite directions. Because you can measure the distance
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Geometry is simply the study of space. There are Euclidean and Non-Euclidean Geometries. Euclidean geometry is the most common and is the basis for other Non-Euclidean types of geometry. Euclidean geometry is based on five main rules‚ or postulates. Differences in these rules are what make new kinds of geometries. There is Euclidean‚ Elliptic‚ and Hyperbolic Geometry. Euclidean geometry is the study of flat space and was invented by Euclid‚ a mathematician from Alexandria‚ in 330 B.C. Euclid described
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HYPERBOLIC GEOMETRY AND OMEGA TRIANGLES Hyperbolic geometry was first discovered and explored by Omar Khayyam in the 9th century and Giovanni Gerolamo Saccheri in the 15th century. Both were attempting to prove Euclid’s parallel postulate by proving the concept of hyperbolic geometry to be inconsistent‚ and ironically they discovered it to be a new type of geometry. It wasn’t until the 19th century that it became fully developed with help from Karl Friedrich Gauss‚ Janos Bolyai‚ and Nikolai
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Question:An architect designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is 625y^2 - 400x^2=250‚000‚ where x and y are in yards. How far apart are the houses at their closeset point? Answers:625y^2 - 400x^2=250‚000 y^2 / 20^2 - x^2 / 25^2 = 1 The closest two points on separate branches are the vertices‚ and their separation is 2 * 20 = 40yd. I find the question a little confusing‚ though. Question:LORAN (long distance radio navigation)
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C OORDINATE GEOMETRY COORDINATE GEOMETRY 155 7 7.1 Introduction In Class IX‚ you have studied that to locate the position of a point on a plane‚ we require a pair of coordinate axes. The distance of a point from the y-axis is called its x-coordinate‚ or abscissa. The distance of a point from the x-axis is called its y-coordinate‚ or ordinate. The coordinates of a point on the x-axis are of the form (x‚ 0)‚ and of a point on the y-axis are of the form (0‚ y). Here is a play for you. Draw a set
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