{"id":12645,"date":"2024-03-04T11:56:39","date_gmt":"2024-03-04T06:26:39","guid":{"rendered":"https:\/\/tsboardsolutions.in\/?p=12645"},"modified":"2024-03-05T14:22:18","modified_gmt":"2024-03-05T08:52:18","slug":"ts-10th-class-maths-notes-chapter-7","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.in\/ts-10th-class-maths-notes-chapter-7\/","title":{"rendered":"TS 10th Class Maths Notes Chapter 7 Coordinate Geometry"},"content":{"rendered":"

We are offering TS 10th Class Maths Notes<\/a> Chapter 7 Coordinate Geometry to learn maths more effectively.<\/p>\n

TS 10th Class Maths Notes Chapter 7 Coordinate Geometry<\/h2>\n

\u2192 A French mathematician Rene Descartes (1596 – 1650) has developed the study of Co-ordinate Geometry.<\/p>\n

\u2192 The cartesian plane is also called co-ordinate plane or xy plane.<\/p>\n

\u2192 The X-co-ordinate is called the Abscissa and the y-co-ordinate is called the ordinate.<\/p>\n

\u2192 The intersection of x-axis and y-axis is called the origin. The co-ordinates of origin = 0 (0, 0).<\/p>\n

\u2192 Area of Rhombus = \\(\\frac{1}{2}\\) \u00d7 product of its diagonals.<\/p>\n

\u2192 Area of a triangle = \\(\\frac{1}{2}\\) \u00d7 base \u00d7 height.<\/p>\n

\u2192 The distance between two points P(x1<\/sub>, y1<\/sub>) and Q(x2<\/sub>, y2<\/sub>) is \\(\\sqrt{\\left(x_2-x_1\\right)^2+\\left(y_2-y_1\\right)^2}\\)<\/p>\n

\u2192 The distance of a point (x, y) from the origin is \\(\\)<\/p>\n

\u2192 The distance between two points (x1<\/sub>, y1<\/sub>) and (x2<\/sub>, y2<\/sub>) on a line parallel to Y – axis is |y2<\/sub> – y1<\/sub>|.<\/p>\n

\u2192 The distance between two points (x1<\/sub>, y1<\/sub>) and (x2<\/sub>, y2<\/sub>) on a line parallel to X-axis is |x2<\/sub> – x1<\/sub>|.<\/p>\n

\u2192 The co-ordinates of the point P(x, y) which divides the line segment joining the points A(x1<\/sub>, y1<\/sub>) and B(x2<\/sub>, y2<\/sub>) internally in the ratio m1<\/sub> : m2<\/sub> are
\n\\(\\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]\\)<\/p>\n

\"TS<\/p>\n

\u2192 The midpoint of the line segment joining the points P(x1<\/sub>, y1<\/sub>) and Q(x2<\/sub>, y2<\/sub>) is
\n\\(\\left(\\frac{x_1+x_2}{2}, \\frac{y_1+y_2}{2}\\right)\\)<\/p>\n

\u2192 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.<\/p>\n

\u2192 The vertices of \u0394ABC are A(x1<\/sub>, y1<\/sub>), B(x2<\/sub>, y2<\/sub>) and C(x3<\/sub>, y3<\/sub>), then the co-ordinates of the centroid of the \u0394ABC is \\(\\left[\\frac{x_1+x_2+x_3}{3}, \\frac{y_1+y_2+y_3}{3}\\right]\\)<\/p>\n

\u2192 The area of the triangle formed by the points (x1<\/sub>, y1<\/sub>) (x2<\/sub>, y2<\/sub>) and (x3<\/sub>, y3<\/sub>) is the numerical value of the expression
\n\\(\\frac{1}{2}\\)|x1<\/sub>(y2<\/sub> – y3<\/sub>) + x2<\/sub>(y3<\/sub> – y1<\/sub>) + x3<\/sub>(y1<\/sub> – y2<\/sub>)|.<\/p>\n

\u2192 Area of a triangle formula or Heron’s Formula A = \\(\\sqrt{s(s-a)(s-b)(s-c)}\\)
\nS = \\(\\frac{a+b+c}{2}\\)<\/p>\n

\u2192 Slope of the line (m) = \\(\\frac{y_2-y_1}{x_2-x_1}\\)<\/p>\n

Important Formula:<\/p>\n