Question

Class 9th
Mathematics
Chapter 3 - Coordinate Geometry
Formulas Needed . Give 1 example for each Formuals

Note : Don't copy, Don't spam .

Quality answer with good explanation will be Brainliest .​ .​

Answer 1

Step-by-step explanation:

Coordinate Geometry:-

• Coordinate Geometry was introduced by Rene Descartes , a French mathematician.

• To locate the exact position of a point on a number line we need only single reference.

• To describe the exact position of a point on a Cartesian plane we need two references.

• The two perpendicular lines taken in any direction are referred to as coordinate axes.

• The horizontal line is called X- axis

• The vertical line is called Y-axis.

• The intersection of X and Y axes is called the Origin.

• The coordinates of the Origin is (0,0)

• The distance of a point from Y- axis is called X- coordinate or Abscissa.

• Ths distance of a point from X - axis is called y-coordinate or Ordinate .

Ex:-

In (8,9) ,abscissa = 8 and Ordinate = 9

• The coordinate plane is divided into four quadrants namely Q1,Q2,Q3,Q4 .

• The signs of coordinates of a point are as follows:
• Q1---->(+,+)

Ex:- (2,3)

• Q2---->(-,+)

Ex:-(-2,3)

• Q3----->(-,-)

Ex:-(-2,-3)

• Q4------>(+,-)

Ex:-(2,-3)

• The x-coordinate of a point on Y - axis is Zero.

Ex:- (0,3)

• The y-coordinate of a point on X-axis is zero.

Ex:- (3,0)

• Equation of X-axis is y=0

• Equation of Y-axis is X=0

• In a Coordinate plane (x1,y1) ≠(x2,y2) unless x1=x2 and y1=y2

• (a,b)≠(b,a)

Additional information:-

• The distance between the origin and the point (x,y) is √(x^2+y^2) units
• The distance between the points (x1, y1)and (x1, y2) is |y2-y1| units
• The distance between the points (x1, y1) and (x2, y1) is |x2-x1| units
• The distance between the points (x1, y1) and (x2, y2) is √[(x2-x1)^2+(y2-y1)^2] units
• The slope of the line joining the points x1, y1) and (x2, y2) is (y2-y1)/(x2-x1)
• (x1, y1) and (x2, y2) are the two points joining a linesegment then the mid point is. ( (x1+x2)/2 ,(y1+y2)/2 )
• Slope =m= Tan θ
• Coordinates of a centroid of a triangle formed by the points (x1, y1) ,(x2, y2) and (x3, y3) is ((x1+x2+x3)/3 ,(y1+y2+y3)/3)
• Area of a triangle formed by the points. (x1, y1) ,(x2, y2) and (x3, y3) is
• (1/2)| x1(y2-y3)+x2(y3-y1)+x3(y1-y2) | sq.units
• Section formula = ((m1x2+m2x1)/(m1+m2), (m2y1+m2y1)/(m1+m2)
• The points lie on the same line are called collinear points.
• The points which divides the given line segment into three equal parts or in the ratio 2:1 or 1:2 are called Trisectional points.