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Flash Back from Class IX Coordinate geometry notes
- We require two perpendicular axes to locate a point in the plane. One of them is horizontal and other is Vertical
- The plane is called Cartesian plane and axis are called the coordinates axis
- The horizontal axis is called x-axis and Vertical axis is called Y-axis
- The point of intersection of axis is called origin.
- The distance of a point from y axis is called x –coordinate or abscissa and the distance of the point from x –axis is called y – coordinate or Ordinate
- The x-coordinate and y –coordinate of the point in the plane is written as (x, y) for point and is called the coordinates of the point
- The Origin has zero distance from both x-axis and y-axis so that its abscissa and ordinate both are zero. So the coordinate of the origin is (0, 0)
- A point on the x –axis has zero distance from x-axis so coordinate of any point on the x-axis will be (x, 0)
- A point on the y –axis has zero distance from y-axis so coordinate of any point on the y-axis will be (0, y)
- The axes divide the Cartesian plane in to four parts. These Four parts are called the quadrants
- The coordinates of the points in the four quadrants will have sign according to the below table
Quadrant
|
x-coordinate
|
y-coordinate
|
Ist Quadrant
|
+
|
+
|
IInd quadrant
|
-
|
+
|
IIIrd quadrant
|
-
|
-
|
IVth quadrant
|
+
|
-
|
Distance formula
Distance between the points AB is given by
Distance of Point A from Origin
Section Formula
A point P(x,y) which divide the line segment AB in the ratio m
1 and m
1 is given by
The mid point P is given by
Area of Triangle ABC
Area of triangle ABC of coordinates A(x
1,y
1) , B(x
2,y
2) and C(x
3,y
3) is given by
For point A,B and C to be collinear, The value of A should be zero
How to Solve the line segment bisection ,trisection and four-section problem's
1) You will be given coordinates of the two point A , B
2) If the problem is to find bisection, then you can simply found the mid point using
3) If the problem is to find trisection(three equal parts of the line ).Let us assume the point are P and Q, then AP=PQ=QB
Now P divides the line AB into 1:2 part
While Q divides the line AB into 2:1 part
So we can use section formula to get the coordinate of point P and Q
4) If the problem is to finnd four equal parts .Let us assume the point are P ,Q And R such that AP=PQ=QR=RB
Now P divides the line AB into 1:3 part
Q divides the line AB into 1:1 part
R divides the line AB into 3:1 part
So we can use section formula to get the coordinate of point P ,Q and R
How to Prove three points are collinear
1) We need to assume that if they are not collinear,they should be able to form triangle.
We will calculate the area of the triangle,if it comes zero, that no triangle can be found and they are collinear
How to solve general Problems of Area in Coordinate geometry
| Area of Triangle |
Three vertices will be given,you can calculate the area directly using formula |
| Area of Square |
Two vertices will be given, we can calculate either side or diagonal depending on vertices given and apply the square area formula |
| Area Of rhombus |
Given: all the vertices coordinates
Two ways
1) Divide the rhombus into two triangle. Calculate the area of both the triangle and sum it
2) Calculate the diagonal and apply the Area formula
|
| Area of parallelogram |
Three vertices are sufficent to find the area of parallelogram
Calculate the area of the traingle formed by the three verticles and double it to calculate the area of parallelogram
|
| Area of quadilateral |
Given: all the vertices coordinates
Divide into two triangle. Calculate the area seperately and sum it
|
Class 10 Maths
Class 10 Science
