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S.L. Loney The Straight Line Rectangular Coordinates Solutions (Chapter 4)

SL Loney Elements of Coordinate Geometry Solutions Chapter 4 deal with the concepts related to straight lines. Practising these solutions, you will be able to build a strong grip in maths and will result in better performance of your academic exams as well as competitive exams like NEET and IIT JEE. All these SL Loney Solutions for Elements of Coordinate Geometry are prepared by the subject matter experts at Instasolv to provide you with a better understanding of the chapter ‘The Straight Line – Rectangular Coordinates’.

Some of the important topics of SL Loney The Straight Line – Rectangular Coordinates Solutions are the properties of straight lines, rectangular coordinates, coordinate geometry, the line at infinity, equation of the straight line, equation of axes, bisectors of angles between straight lines, length of perpendicular, and the angle between straight lines. We have covered all the topics in these solutions so you can prepare for your entrance exams with ease.

Chapter 4 ‘The Straight Line – Rectangular Coordinates’ has 4 main exercises with a total of 105 problems based on these straight lines concepts. Solving these questions will help you practice the concepts easily and prepare well for your exams. In order to score better marks, we would highly recommend you to follow our SL Loney Elements of Coordinate Geometry Solutions for Chapter 4 provided by Instasolv. You can follow these solutions at any time for free.

Important Topics for SL Loney Elements of Coordinate Geometry Solutions Chapter 4: The Straight Line – Rectangular Coordinates

Straight Line

A line is the set of all points between and increasing away from two points. A line may be a basic body that doesn’t have formal properties of length, its single dimension.

Properties of Straight Lines

The properties of straight lines are characterized below:

  • Straight lines are one-dimensional
  • They must be vertical, diagonal, or horizontal
  • Both ends of a straight line can be extended in two directions forever
  • When drawing an angled arc from one point to another a straight line makes a 180-degree angle

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.

Coordinate Geometry

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.

Line at Infinity

The line at infinity is defined as a projective line that’s added to the real plane so as to offer closure to, and eliminate the exceptional cases from, the incidence properties of the resulting projective plane. The ideal line is also referred to as the line at infinity.

Equation of a Straight Line

The lines on the coordinate plane are often described by the equation, y = mx + b where m is the slope of the line, and b is that the intercept.

Bisectors of Angles between Straight Lines

The bisectors of angles between straight lines are defined as the line which bisects the angle between the two lines and the locus of those angle to some extent is equidistant from the two lines.

Equation of Axes

Equation of axes refers to the equation of x-axis, y-axis, and z-axis. Equation of y-axis refers to a line which 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.

Length of Perpendicular

The length between perpendiculars refers to the length of a ship along the summer load line from the headlong surface of the stem, or foremost bow perpendicular member, to the after the surface of the sternpost, or foremost stern vertical member.

The Angle between Straight Lines

The angle between directions vectors of the lines is the angle between two lines. If p = {px ,py, pz} and q = {qx , qy , qz} is the direction vectors of lines, then

The direction vectors are also perpendicular if two lines are perpendicular to each other.

p.q = pxqx + pyqy + pzqz = 0

The direction vectors are proportional if two lines are parallel to each other.

P = cq

Exercise-wise Discussion for SL Loney Elements of Coordinate Geometry Solutions Chapter 4: The Straight Line – Rectangular Coordinates

Exercise 1 – Very Short Answer Type Questions

SL Loney Coordinate Geometry Solutions for Chapter 4 Exercise 1 has a total of 29 questions. In these questions, you need to find the equation to the straight line.

Exercise 2 – Short Answer Type Questions

This exercise consists of a total of 21 questions based on the angles between the pairs of straight lines. All these questions are explained in detail.

Exercise 3 – Long Answer Type Questions

This exercise set has a total of 11 questions where you need to find the length of the perpendicular drawn from the points given upon the straight line. Practising these questions will help you in your JEE exams preparation.

Exercise 4 – High-Level Thinking Questions

Exercise 4 of SL Loney Solutions for ‘The Straight Line – Rectangular Coordinates’ contains a total of 45 questions. These questions are based on the main topic of the chapter that is bisectors of angles between straight lines. Practice well to make your concepts stronger.

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The main benefits of SL Loney Elements of Coordinate Geometry Solutions for Chapter 4 are provided below:

  • The SL Loney Solutions for Elements of Coordinate Geometry Chapter 4 contain conceptual sums, which cover your academic and competitive exams like NEET, JEE Mains, and JEE Advance.
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