Maths Notes Maths Notes for Shear and Stretch Stretch • The transformation consists of:o o • The invariant line Scale factor For stretch‚ the transformation takes place perpendicular to the invariant line. • Scale factor(K) = 4 3 2 1 -2 -1 0 -1 -2 -3 1 2 3 = Y 4 X Invariant line In the above example‚ the x-axis is the invariant line and the object lies on (1‚1). Thus‚ =1 The scale factor is given to us as K = 3 1 Maths Notes Thus‚ acc. to the formula given
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What is the reciprocal of the tangent function? Answer: Cotangent 5. What is the numbers used to locate a point in space? Answer: Coordinates 6. What is the point at which the axes of a coordinate system cross; the point (0‚0) in the Cartesian coordinate system? Answer: Origin 7. Any one of the four regions into which coordinates axis divide a plane. Answer: Quadrant 8. What is the quotient of two polynomials? Answer: Rational Expression 9. What is
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Math - Problem Solving : Geometry Problem Solving | | | | | | | | | | | | | | | | | | | | |Student
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Geometry Problems Amir Hossein Parvardi∗ January 9‚ 2011 Edited by: Sayan Mukherjee. Note. Most of problems have solutions. Just click on the number beside the problem to open its page and see the solution! Problems posted by different authors‚ but all of them are nice! Happy Problem Solving! 1. Circles W1 ‚ W2 intersect at P‚ K. XY is common tangent of two circles which is nearer to P and X is on W1 and Y is on W2 . XP intersects W2 for the second time in C and Y P intersects W1 in B. Let
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© cxcDirect Institute CSEC MATHEMATICS Past Paper Solution – May 2014 cxcDirect Institute © All rights reserved. No part of this document may be reproduced without the written consent of the Author cxcDirect Institute Email: admin@cxcDirect.org Website: www.cxcDirect.org All Help videos are free‚ and can be viewed from our website © cxcDirect Institute © cxcDirect Institute ** Please see the original past paper for the questions. Only the answers will be provided as per
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clear that the coordinates of point C are (0‚ a)‚ while the coordinates of point B are (0‚ –a). Page 2 of 68 Class XI Chapter 10 – Straight Lines Maths It is known that the line joining a vertex of an equilateral triangle with the mid-point of its opposite side is perpendicular. 20 14 Hence‚ vertex A lies on the y-axis. On applying Pythagoras theorem to ∆AOC‚ we obtain ⇒ (2a)2 = (OA)2 + a2 ⇒ 4a2 – a2 = (OA)2 ⇒ OA = IT ⇒ (OA)2 = 3a2 © (AC)2 = (OA)2 + (OC)2 ∴Coordinates of point A =
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Jesus Toro-Sanchez 03/13/2013 Math 60 Chapter 4 Writing Assignment 1) Explain how to plot a point in the rectangular coordinate system. Give example with your explanation. a. In order to plot a point in the coordinate system‚ you will need the X coordinate as well as the Y coordinate. For example‚ the point (3‚5) can be plotted be going right on the X axis 3 points‚ and going up on the Y axis 5 points. Remember the opposite goes for negatives. 2) How many Points are needed to graph
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Course Code: Math 1 Course Title: College Algebra Year: 1st Year Topic: Functions Designer: Frago‚ Christine Joy S. Stage 1 – Desired Results Established Goals: This section aims to: 1. distinguish a function from a mere relation; and 2. find the domain and range of functions or relations Understandings: Students will understand… the definition of relation the definition of function the relationship between relation and function Essential Questions: Is the relation a function
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Cartesian Vectors Addition and Subtraction of Cartesian Vectors Position Vectors Force Vector Directed along a Line Dot Product Copyright © 2010 Pearson Education South Asia Pte Ltd 2.5 Cartesian Vectors • Right-Handed Coordinate System A rectangular or Cartesian coordinate system is said to be right-handed provided: – Thumb of right hand points in the direction of the positive z axis – z-axis for the 2D problem would be perpendicular‚ directed out of the page. Copyright © 2010 Pearson Education
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Cartesian Plane and Coordinate System Introduction: The Cartesian Plane consists of two perpendicular number lines. The vertical y-axis‚ and the horizontal x-axis. These two lines intersect at a point called the origin. This system establishes a correspondence between points in the plane and pairs of real numbers. For every pair of real numbers‚ there corresponds a point in the plane. The Cartesian Plane also consists of four quadrants. The top-right quarter is Quadrant I‚ the top-left is Quadrant
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