Coordinate Geometry - Revision Notes

 CBSE Class 10 Mathematics

Revision Notes
CHAPTER 07
COORDINATE GEOMETRY

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1. Distance Formula
2. Section Formula
3. Area of a Triangle

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1. Distance Formula: The length of a line segment joining A and B is the distance
   between two points A(x1,y1)$A(x_1,y_1)$ and (x2,y2)$(x_2,y_2)$ is (x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
    
2. The distance of a point (x,y)$\left(x,y\right)$ from the origin is (x2+y2)−−−−−−−√$\sqrt{(x^2+y^2)}$. The distance of P from x-axis is y units and from y-axis is x-units.
    
3. Section Formula: The co-ordinates of the points p(x, y) which divides the line segment joining the points A(x1,y1)$A(x_1,y_1)$ and B(x2,y2)$B(x_{2,}{y}_2)$ in the ratio m1:m2$m_1:m_2$ are (m1x2+m2x1m1+m2,m1y2+m2y1m1+m2)$\left(\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2},\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}\right)$ we can take ratio as k:1,k=m1m2$k:1,k=\frac{m_1}{m_2}$
    
4. Mid-point Formula: The mid-points of the line segment joining the points P(x1,y2)andQ(x2,y2)$P(x_1,y_2)andQ(x_2,y_2)$ is (x1+x22,y1+y22)$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$
    
5. Area of a Triangle: The area of the triangle formed by the points (x1,y1),(x2,y2)and(x3,y3)$(x_1,y_1),(x_2,y_2)and(x_3,y_3)$ is the numeric value of the expressions 12|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|$\frac{1}{2}\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|$.
    
6. If three points are collinear then we cannot draw a triangle, so the area will be zero i.e. |x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|=0