Coordinate geometry class 10 formulas 2021-22[PDF Included ]

In class ix, we have learned to locate a point on the plane. To locate a point, we need to draw a pair of mutually perpendicular lines which is known as Coordinate Axes. The Horizontal line is known as the X-axis and the Vertical line is known as the Y-axis. The intersection point of these coordinate axes is known as ORIGIN which coordinates taken as (0,0) and it is used as a reference point to locate other points in the Coordinate Plane. The coordinates axes divide a plane into four parts which are known as Quadrants

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Here is the Sign Convention of quadrants in the plane ;

I quadrant : x>0 ,y>0

II quadrant: x<0,y>0

III quadrant : x<0 ,y<0

IV quadrant : x>0 ,y<0

Coordinate Quadrant

You must be familiar with the given terms to Understand the Basic formulas of Coordinate Geometry.

 

The important points for class 10 coordinate geometry 

1. The distance of a point from the y-axis is called  X-coordinate or Abscissa.

Or 

    The abscissa of a point is its Perpendicular Distance from the y-axis.

X-coordinate or abscissa

2. The distance of a point from the x-axis is called Ordinate.

Or 

     The Ordinate of a point is its perpendicular distance from the x-axis.

Y-coordinate or Ordinate

3. The coordinates of a point on the x-axis are of the form (x,0).

 

4 . The coordinates of a point on the y-axis are of the form (0,y).

 

5. The coordinates of Every point in the Coordinate Plane are Unique.

6. The set of all ordered pairs (x,y) of Real numbers is called the Cartesian plane and it is denoted by R².

7. The Ordinate of every point situated above the x-axis is “Positive” and that of every point below the x-axis is “Negative”.

8. The Abscissa of every point situated on the right side of the y-axis is positive and the abscissa of every point situated on the left side of the y-axis is negative.

Coordinate geometry class 10 hot questions list 

Coordinate geometry class 10 formulas list

1. Distance formula

The distance formula is used to calculate the distance and length between two points. Let P and Q are the points whose coordinates are P(x,y), Q (X, Y).

Distance Formula

The length of line PQ is given by =√(X-x)²+(Y-y)².

Note: The distance between a point and Origin is given by √x²+y².

2. Section formulae

This formula is used to find the coordinate of points on any line.

Section Formula

 

 

In the given figure, AB is the line segment and P is a point on it which divide the given line segment into the ratio of m and n . Then, the coordinates of point P is given by

= (\frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n})

Application of section formula

Suppose ,we have a triangle ΔABC whose vertices Coordinates are A(x,y),B(X,Y) ,C(a,b) .Coordinates of its centroid can be find out using Section Formula .

Centroid of triangle using section formula

Centroid Coordinates of ΔABC=\frac{x+X+a}{3},\frac{y+Y+b}{3}

3. Area of triangle

In earlier classes, we have studied several formulas to calculate the “Area of a Triangle” Such as,

= \frac{1}{2}×base×height

= Heron’s Formula, etc 

But above formulas are applicable when the length of sides is given otherwise we cannot calculate. Here we will find the area of the triangle by Coordinates of the vertices of a triangle, not by the length of the side

Let see...

Area of triangle using section formula

Suppose we have a triangle ΔABC whose vertices coordinates are A(x,y),B(X,Y) ,C(a,b) .Then the area of this triangle is given by 

Area( ΔABC)= \frac{1}{2}|x(y-b)+X(b-y)+a(y-Y)|

 

 

 

 

 

 

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