RS Aggarwal Solutions Class 8 Maths Chapter 22 Introduction To Coordinate Geometry (Updated For 2024)

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RS Aggarwal Solutions Class 8 Maths Chapter 22 Introduction To Coordinate Geometry

RS Aggarwal Solutions Class 8 Maths Chapter 22 Introduction To Coordinate Geometry – Overview

In RS Aggarwal Solutions Class 8 Maths Chapter 22, you will learn about coordinate geometry, based on analytic geometry that uses coordinate points to find the distance between any two points, get the midpoint of a line, divide lines, and calculate a triangle area in the cartesian plane, and more.

You must know the key terms used in this chapter.

• Coordinate geometry: It is a study of geometry where coordinates are used to define a point. This helps to find the exact position of a point in a coordinate plane. 
• Coordinate and Coordinate Plane: A cartesian plane (or a 2D plane) is divided into 4 quadrants where 2 axes are perpendicular to each other, i.e., x-axis and y-axis where the two lines XOX’ and YOY’ are perpendicular to each other. 

   

1. XOX’ represents the x-axis which is horizontal to the cartesian plane
2. YOY’ represents the y axis which is vertical to the cartesian plane

• Quadrants: The four quadrants which are present in the cartesian plane, mentioned below: 

1. Quadrant 1- XOY, sign (+,+)
2. Quadrant 2- YOX’ , sign (-,+)
3. Quadrant 3- X’OY’ , sign (-,-)
4. Quadrant 4- Y’OX, sign (+,-)

• Ordered Pair: An ordered pair of coordinates is any point in the cartesian plane is represented in the form of (x,y), where x is present in the x-coordinate called as abscissa of the point, and y is present at y-coordinate known as ordinate of the point. 
• Origin: The origin is a point at which both the axis intersects with each other.

Equation Of A Line In Cartesian Plane

As per the RS Aggarwal Solutions Class 8 Maths Chapter 22 Introduction To Coordinate Geometry, an equation of a line can be represented in various ways, mentioned below:

• The General Form of A Line: The general form of a line can be written as Ax+By+C= 0
• Slope-Intercept Form: If x and y are coordinates of a point from where a line passes with am being the slope of a line which c is the y-intercept, then the equation of a line is written as: 

y = mx+c

• Intercept Form: If x and y are the x-intercept and y-intercept of a line, then the equation of a line  is written as

y = mx+c

• The Slope of a Line: let the general form of a line is Ax+By+C= 0, the slope can be found by converting the general form of a line to slope-intercept form. 

Ax+By+C= 0

or, By= -Ax -C

or, y = -A/B x – C/ B

Comparing this equation with the slope-intercept equation

m= -A/B

Theorems And Formulae

• Distance Formula: The distance between two points, i.e., A and B,

  with coordinates (x1, y1 ) and ( x2, y2 ) respectively can be calculated as

  d= √(X2−X1)2+(Y2−Y1)2

• Midpoint Theorem: The midpoint, M(x,y) of a line connecting two points, i.e., A and B with coordinates( x1, y1 ) and ( x2, y2)  respectively  is given as 

  M (x,y) = (x1+x2/2,y1+y2/2)

• Angle Formula: Two lines A and B with slopes m1 and m2 respectively where θ is the angle between these two lines. The angle between them is given as

  Tan θ = m1−m2/1+m1m2

  If the two lines are parallel to each other then: m1 = m2 = m

  If the two lines are perpendicular to each other then: m1 x m2 = -1

• Section Formula: Line A and B which have (x₁,y₁) and x₂,y₂ as coordinates respectively and P point divides the lines into m:n ratio, then the coordinates of point P are:

m:n (internal) (mx2+nx1m+nmx2+nx1/m+n, my2+ny1m+nmy2+ny1/m+n)

m:n (external) (mx2−nx1m−nmx2−nx1/m−n, my2−ny1m−nmy2−ny1/m−n)

Area of triangle in a Cartesian plane: The area of a triangle whose vertices are x1,y1 , x2,y2 and x3,y3 is 

½  [x1(y2- y3) + x2 (y3-y1) + x3 (y1-y2)]

If the area of the triangle whose vertices are x1,y1, x2,y2, and x3,y3 is 0, then the 3 points are collinear. 

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