We are offering TS 10th Class Maths Notes Chapter 7 Coordinate Geometry to learn maths more effectively.

## TS 10th Class Maths Notes Chapter 7 Coordinate Geometry

→ A French mathematician Rene Descartes (1596 – 1650) has developed the study of Co-ordinate Geometry.

→ The cartesian plane is also called co-ordinate plane or xy plane.

→ The X-co-ordinate is called the Abscissa and the y-co-ordinate is called the ordinate.

→ The intersection of x-axis and y-axis is called the origin. The co-ordinates of origin = 0 (0, 0).

→ Area of Rhombus = \(\frac{1}{2}\) × product of its diagonals.

→ Area of a triangle = \(\frac{1}{2}\) × base × height.

→ The distance between two points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) is \(\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)

→ The distance of a point (x, y) from the origin is \(\)

→ The distance between two points (x_{1}, y_{1}) and (x_{2}, y_{2}) on a line parallel to Y – axis is |y_{2} – y_{1}|.

→ The distance between two points (x_{1}, y_{1}) and (x_{2}, y_{2}) on a line parallel to X-axis is |x_{2} – x_{1}|.

→ The co-ordinates 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

\(\left[\frac{m_1 x_2+m_2 x_1}{m_1+m_2}, \frac{m_1 y_2+m_2 y_1}{m_1+m_2}\right]\)

→ The midpoint of the line segment joining the points P(x_{1}, y_{1}) and Q(x_{2}, y_{2}) is

\(\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\)

→ The point of intersection of the medians of a triangle is called the centroid. It is usually denoted by G. it divides each median in the ratio 2 :1.

→ The vertices of ΔABC are A(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}), then the co-ordinates of the centroid of the ΔABC is \(\left[\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right]\)

→ The area of the triangle formed by the points (x_{1}, y_{1}) (x_{2}, y_{2}) and (x_{3}, y_{3}) is the numerical value of the expression

\(\frac{1}{2}\)|x_{1}(y_{2} – y_{3}) + x_{2}(y_{3} – y_{1}) + x_{3}(y_{1} – y_{2})|.

→ Area of a triangle formula or Heron’s Formula A = \(\sqrt{s(s-a)(s-b)(s-c)}\)

S = \(\frac{a+b+c}{2}\)

→ Slope of the line (m) = \(\frac{y_2-y_1}{x_2-x_1}\)

Important Formula:

- AB = \(\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
- Point (x, y) form the origin is \(\sqrt{x^2+y^2}\)
- Mid Point = \(\left[\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right]\)
- Centroid = \(\left[\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right]\)
- Area = \(\frac{1}{2}\)|x
_{1}(y_{2}– y_{3}) + x_{2}(y_{3}– y_{1}) + x_{3}(y_{1}– y_{2})|. - Heron’s Formula A = \(\sqrt{S(S-a)(S-b)(S-c)}\)
- S = \(\frac{a+b+c}{2}\)
- Slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

Flow Chat:

Rene Descartes (1596 – 1650):

- Rene Descartes was a French Mathematician.
- Rene Descartes is a Father of Modern Mathematics.
- The Cartesian co-ordinate system – allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two – dimensional co-ordinate system was named after him.
- Descartes theory provided the basis for the calculus of Newton and Leibnitz.