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RS Aggarwal Class 10 Chapter 6 Solutions (Coordinate Geometry)

RS Aggarwal Class 10 Maths Solutions Chapter 6 ‘Coordinate Geometry’ is a great study material for your board exams. In this chapter of RS Aggarwal Class 10 Maths Solutions, you will revise the fundamentals of two-dimensional geometry. The main topics covered in the chapter are the distance between any two points on the plane, section formula, and the midpoint formula. In the end, you will also learn about the centroid of a triangle and calculating the area of a triangle. 

This chapter covers all the basic to difficult level questions for two-dimensional coordinate geometry. This chapter has 5 well-thought exercises and a total of 157 questions for complete revision and better learning. With the help of these exercises, you will be able to find the distance between two points on a graph, finding the coordinates of a point when the distance between points is given, and finding the coordinates of a point if it lies on a circle. 

The best way to improve your understanding of the chapter and ensure that you are able to solve all kinds of problems related to the chapter, you must refer to our RS Aggarwal Solutions. Our stepwise approach will enable you to grasp all the concepts of the chapter. They will help in improving your efficiency in solving problems and enable you to revise the topics easily before exams.  

Important Topics for RS Aggarwal Class 10 Maths Solutions Chapter 6: Coordinate Geometry

Basics of a Cartesian Plane

Any point on a given plane can be located by a pair of numbers that are known as the coordinates. The distance of a given point from the y-axis is called abscissa or x-coordinate. The length of any given point from the x-axis is known as ordinates or y-coordinate.

Distance Formula: The following formula gives the distance of any two points A (x1, y1) and B(x2, y2)-

d=√[x2-x1)2+(y2-y1)2]

Section Formula

If any point P(x,y) that divides the line segment which is joining A(x1, y1) and B(x2, y2) internally in let’s suppose the ratio m:n, then, the coordinates of the point P can be calculated by the section formula given as-

P(x,y)= {(mx2+nx1)/(m+n), (my2+ny1)/(m+n)}

Mid-Point

The midpoint of the line segment always divides it in the ratio of 1:1. Therefore the coordinates of that midpoint of the line segment joining points A(x1, y1) and B(x2, y2) is given by the following formula-

p(x,y) = [ (x1+x2)/2 , (y1+y2)/2 ]

Centroid of a triangle

If some points A(x1, y1), B(x2, y2) and C(x3, y3) are the three vertices of a triangle ABC, then we can calculate the coordinates of its centroid which is given as-

C(x,y) = [ (x1+x2+x3)/3 , (y1+y2+y3)/3 ]

Area from Coordinates

The area can be calculated from a formula if the vertices of the triangle are given. If we suppose as A(x1,y1), B(x2,y2) and C(x3,y3) be the three vertices of a Δ ABC, then the area is calculated by the following formula-

A= 1/2[x1(y2−y3)+x2(y3−y1)+x3(y1−y2) ]

Important Notes 

  1. If we take the points A, B, and C in the anticlockwise direction, then the area obtained will be positive. 
  2. If we take the points in the clockwise direction, then the area will come out to be negative. Therefore we take the absolute value every time we calculate the area.
  3. If the area of a triangle is coming out to be zero, then it means that the three points are collinear.

Exercise Discussion of RS Aggarwal Class 10 Maths Solutions Chapter 6: Coordinate Geometry

Exercise 6A 

  • It contains 32 problems. The questions are mainly about finding the distance between given points or from the origin. 
  • Some questions are also based on finding the coordinates of the points and proving the collinearity.

Exercise 6B  

  • It has 30 questions which are mainly based on section formula. Here distance is to be calculated given the ratio in which coordinates divide. 
  • Some questions are about finding the midpoint as well.

Exercise 6C

  • It contains 22 problems that are based on calculating the area of the triangle and quadrilateral using coordinates. 
  • Some questions are about the collinearity and the ratio of areas.

Exercise 6D 

  • It consists of 17 questions which are based on finding the median of a triangle and diagonal of a quadrilateral.

Multiple-Choice Questions

  • At last, there are 34 MCQs given in the chapter that is based on all the concepts of the chapter such as the midpoint theorem, collinear points, coordinates of polygons, and equidistant points. 

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