AP SSC Class 10 Maths Chapter 7 Coordinate Geometry

Coordinate Geometry is an important branch of mathematics that provides a connection between geometry and algebra in the form of graphs of lines and curves. It helps us locate points on a graph and its applications are spread across fields like dimensional geometry, calculus, etc.

Important Formulas in Coordinate Geometry

  • The distance between two points \(A(x_{1},y_{1})\) and \(B(x_{2},y_{2})\) is calculated using the formula \(\sqrt{(x_{2}-x_1)^{2}+(y_{2}-y_1)^2}\)
  • The distance between a pointP(x,y) and the origin is given by \(\sqrt{x^2+y^2}\)
  • Distance between two points \(x_{1},y_{1}\) and \(x_{2},y_{2}\) on line parallel to Y-axis is \(\left | y_{2}-y_{1} \right |\).
  • Distance between two points \(x_{1},y_{1}\) and \(x_{2},y_{2}\) on line parallel to X-axis is \(\left | x_{2}-x_{1} \right |\).
  • The coordinates of the point P(x, y) which divides the line segment joining the points A \(x_{1},y_{1}\) and B\(x_{2},y_{2}\)) internally in the ratio \(m_{1}:m_{2}\) are \(\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}},\frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}},\)
  • The mid-point of the line segment joining the points P\(x_{1},y_{1}\) and \(x_{2},y_{2}\) is given by \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)
  • The Heron’s formula or the area of the triangle is given as \(A=\sqrt{S(S-a)(S-b)(S-c))}\) where \(S=\frac{a+b+c}{2}\).
  • A slope of a line is determined as follows \(m=\frac{y_2-y_1}{x_2-x_1}\)

In the next section, let us look at a few solved chapter questions to better understand coordinate geometry.

Class 10 Maths Chapter 7 Coordinate Geometry Solved Questions

    1. Find the distance between the points (0, 0) and (36, 15).

Solution:

The distance between two points (0,0) and (36,15) can be calculated using the formula

D = \(\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^2}\)

Substituting the values in the equation, we get

D = \(\sqrt{(36-0)^2+(15-0)^2}\)

D = \(\sqrt{1296+225}\)

D = \(\sqrt{1521}\)

D = 39

The distance between two points is 39.

    1. Find the midpoint of the line segment joining points (5, 0) and (-3, 6).

Solution: The mid-point of the line segment joining the points P\(x_{1},y_{1}\) and \(x_{2},y_{2}\) is given by \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)

Substituting the values in the formula, we get

\(M(x,y)=(\frac{5+(-3)}{2},\frac{0+6}{2})\) \(M(x,y)= (\frac{2}{2},\frac{6}{2})\) \(M(x,y)= (1,3)\)

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