S.L. Loney Transformation of Coordinates Solutions (Chapter 7)
SL Loney Elements of Coordinate Geometry Solutions Chapter 7 explains how to alter the origin and axes of coordinates without altering the directions of axes. In this chapter, you will further study the fundamental formulae for such a transformation of coordinates. With the help of these SL Loney Solutions for Elements of Coordinate Geometry, you can learn about the various concepts of coordinate geometry.
The main topics of the SL Loney Chapter 7 Transformation of Coordinates Solutions include axes of coordinates, parallel axis, rectangular axis, oblique axes, and change of axes. This chapter also illustrates some interesting concepts which are developed in the numerical problems such as transforming the direction of axes of coordinates, without changing the origin, both systems of coordinates being rectangular. There are around 2 exercises with a total of 12 problems available based on these important topics of the chapter. You can also increase your problem-solving efficiency by referring to the solved examples given in the chapter and practising them.
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Important Topics for SL Loney Elements of Coordinate Geometry Solutions Chapter 7: Transformation of Coordinates
The main concepts of Chapter 7 – Transformation of Coordinates are explained below. Study well to make your concepts stronger.
The study of geometry using the coordinate points is known as coordinate geometry or analytic geometry. Using analytic geometry, it’s possible to seek out the space between two points by dividing lines in ratio m:n, calculating the area of a triangle within the Cartesian plane, finding mid-point of a line, etc.
Axes of Coordinates
Axes of coordinates refer to the axes available on the coordinate plane. It has two main axes including the horizontal axis and the vertical axis. These two axes intersect each other at a point on the surface and this intersecting point is known as the origin.
A coordinate refers to a number. It defines a point on a line. The portion above the origin of the surface will have positive coordinates whereas the portion below the surface is known as negative coordinates. Those axes are known as rectangular coordinate axes because they are located at right angles to each other. The coordinates on them are known as rectangular coordinates.
The coordinate system in two dimensions also known as an orthogonal coordinate system or a rectangular coordinate system. This system is referred to as an ordered pair of perpendicular axes, an orientation for every axis, and a single unit of length for both axes.
The above figure shows an oblique coordinate system. In such systems, the x-coordinate of a point is found by measuring the distance from the point to the y-axis parallel to the x-axis. Similarly, the y-coordinate of a point is found by measuring the distance from the point to the x-axis parallel to the y-axis.
The angle measured in between a line and the x-axis is referred to as the angle of inclination. This angle is always in the middle of 0° and 180° and is calculated counterclockwise from the part of the x-axis to the right of the line. You must note that all horizontal lines have an angle of inclination 0°.
Equation of Axes
Equation of axes refers to the equation of the x-axis, y-axis, and z-axis. Equation of y-axis refers to a line that completely coincides with the y-axis i.e. y-axis itself. So, if we need a line along the y-axis, then both other coordinates must be zero. Therefore, the equation of the y-axis in the second plane is represented as x = 0.
Axis of Rotation
Axis of rotation refers to the straight line through which all static points of a turning rigid body around which all other points of the body move in circles. It keeps on changing over time.
Exercise-wise Discussion for SL Loney Elements of Coordinate Geometry Solutions Chapter 7: Transformation of Coordinates
SL Loney Coordinate Geometry Solutions for Chapter 7 contains 2 exercises with a total of 12 problems. The description of both the exercises is listed below:
Exercise 1 – Short Answer Type Questions
Exercise 1 of SL Loney Transformation of Coordinates Solutions consists of a total of 8 short answer type questions. These questions are based on the important concept of the chapter that is transforming the direction of axes of coordinates, without changing the origin, both systems of coordinates being rectangular. Practising these questions will help you clear your concepts on the transformation of coordinates.
Exercise 2 – Long Answer Type Questions
This exercise consists of a total of 5 questions based on changes of axes. In these questions, you need to change from one set of axes, inclined at an angle, to another set, inclined at another angle, where the origin remains unaltered. They are long answer type questions where you will find detailed solutions to the problems.
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