# S.L. Loney Coordinates. Lengths of Straight Lines and Areas of Triangles Solutions (Chapter 2)

SL Loney Elements of Coordinate Geometry Solutions Chapter 2 is an introduction to a very important area known as Coordinates. It is that division of Maths which is linked to the study of lengths of straight lines and areas of triangles. Some of the main topics included in the questions of the chapter of SL Loney Solutions are axes of coordinates, the origin of coordinates, rectangular axes, Cartesian System of Coordinates, centroid of the triangle, area of a quadrilateral, and more.

Chapter 2 – Coordinates consists of 3 exercises with a total of 82 questions. Solving these problems will help you to clarify your doubts and offer a strong foundation for every concept. It is an important chapter in Maths. So, these books are widely used to excel in your exams as it provides a huge number of questions to practice.

With the help of SL Loney Elements of Coordinate Geometry Solutions for Chapter 2, you should be capable of solving the complex problem in each exercise. Also, the main advantage of referring to these study materials is that they are prepared by the experts at Instasolv as per the CBSE syllabus. These solutions will also help you prepare for JEE Main, JEE Advanced, NEET, and other entrance exams. You can access these solutions at any time for free.

## Important Topics for SL Loney Elements of Coordinate Geometry Solutions Chapter 2: Coordinates – Lengths of Straight Lines and Areas of Triangles

**Coordinates**

Coordinates refer to the distances or angles, signified by numbers that exclusively classify points on two dimensions surfaces (2D) or in space of three dimensions surfaces (3D).

**Cartesian Coordinates**

The two or three straight-line axes that outline the positions of points in 2D or 3D are known as the Cartesian coordinates also called rectangular coordinates. Each and every scale is graduated in increments of uniform size (i.e. all scales are linear).

**Polar Coordinates**

Polar coordinates are referred to as the positions of points in 2D, consistent with the displacement from a central origin and therefore the angular displacement from a reference axis emanating from the origin. In some polar graphs, the radial axis is logarithmic but typically it is linear. The angles are often laid out in degrees or radian s and maybe measured counterclockwise or clockwise from the reference axis.

By the addition of an elevation axis that passes through the origin and perpendicular to the polar plane are the polar coordinates which get extended into 3D to become cylindrical coordinates. In some illustrations the elevation axis is logarithmic but typically it is linear.

**Area of Triangles**

The total space that’s enclosed by any particular triangle is referred to as the area of a triangle. The essential formula to seek out the area of a given triangle is A = 1/2 x b x h, where b is that the base and his that the height of the given triangle, whether it’s isosceles, scalene, or equilateral.

**Coordinate System and Ordered Pairs**

The two-dimensional number line is called a coordinate system, for instance, two perpendicular number lines or axes. The horizontal axis is named the x-axis and therefore the vertical axis is named the y-axis. The origin is defined as the centre of the coordinate system where the lines intersect. (0,0) is referred to as the coordinates of the origin.

An ordered pair consists of the coordinates of one point in the coordinate system. A point is referred by its ordered pair of the created of (x, y). The first number resembles the x-coordinate and the second to the y-coordinate.

**Abscissa and Ordinate**

The abscissa of a point is that the signed measure of its projection on the first axis, whose definite quantity is that distance between the projection and therefore the origin of the axis, and whose sign is given by the location on the projection relative to the origin i.e. after: positive; before: negative.

The ordinate of a point is defined as the signed measure of its projection on the secondary axis, whose definite quantity is that the distance between the origin and the projection of the axis, and whose sign is provided by the location on the projection to the origin i.e. after: positive; before: negative.

**The Centroid of the Triangle**

The point of concurrency of a triangle is known as the centroid. The centroid is described as the triangle’s center of gravity where all the 3 medians intersect.

Some properties of the centroid are:

- The centroid is formed by the intersection of all the 3 medians.
- The concurrency of a triangle is a point of the centroid.
- The centroid is always situated inside the triangle
- The ratio of each and every median is 2:1 which is divided by the centroid.

### Exercise-wise Discussion for SL Loney Elements of Coordinate Geometry Solutions Chapter 2: Coordinates – Lengths of Straight Lines and Areas of Triangles

The solutions of SL Loney Coordinate Geometry Chapter 2 consists of 3 main exercises with a total of 82 questions in the chapter. The detailed description of all these exercises are listed below:

**Exercise 1 – Short Answer Type Questions**

In this exercise of Chapter 2 ‘Coordinates – Lengths of Straight Lines and Areas of Triangles’ there are a total of 27 questions that are based on the concepts of finding the distances between the given pairs of points. Practice well to have a better understanding of the chapter.

**Exercise 2 – Long Answer Type Questions**

Exercise 2 of SL Loney Chapter 2 Solutions contains a total of 15 questions. They are long answer type questions where you have to find the areas of the triangles the coordinates of whose angular points are given.

**Exercise 3 – High Order Thinking Questions**

This exercise consists of a total of 40 questions which are high order thinking questions where you have to lay down the positions of the points whose polar coordinates are provided and other questions based on finding the lengths of the straight lines joining the pairs of points whose polar coordinates are given. Practice the exercise well to score good marks in your competitive exams like JEE and NEET.

## Why Use SL Loney Elements of Coordinate Geometry Solutions Chapter 2: Coordinates – Lengths of Straight Lines and Areas of Triangles by Instasolv?

The main advantage of using the SL Loney Elements of Coordinate Geometry Solutions provided by Instasolv are listed below:

- Along with the SL Loney Elements of Coordinate Geometry Solutions for Chapter 2, Instasolv provides access to solutions for all other chapters as well.
- One of the main advantages of our solutions is that we cover all the questions and sub-questions of the exercises that can be accessed anywhere and anytime.
- Our experts have prepared the solutions to present the complex topics of Chapter 2 in the simplest manner.
- The solutions offered by Instasolv are updated regularly, which is to the point, detailed and at the same time provides an in-depth overview of the chapter.
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