{"id":5740,"date":"2021-12-14T10:48:15","date_gmt":"2021-12-14T10:48:15","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=5740"},"modified":"2021-12-14T13:33:24","modified_gmt":"2021-12-14T13:33:24","slug":"coordinate-geometry-formulas-solved-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/coordinate-geometry-formulas-solved-examples\/","title":{"rendered":"Coordinate geometry \u2013 Formulas, Solved Examples"},"content":{"rendered":"

[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
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Coordinate geometry \u2013 Formulas, Solved Examples<\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|54px|4px|false|false” hover_enabled=”0″ global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

Coordinate Geometry\u00a0<\/b><\/h2>\n

Coordinate geometry is used for the representation of two-dimensional figures in the Cartesian plane. In a Cartesian plane ‘X’ and ‘Y,’ refer to the perpendicular distance of a point from the Y and X-axis respectively. A geometrical figure is represented with the help of points on a coordinate plane in the form of (x,y), where x refers to the x coordinate and y refers to the y coordinate of any point.<\/span><\/p>\n

<\/span><\/p>\n

Formula:<\/b><\/h2>\n

The different formulas associated with coordinate geometry are given below:<\/span><\/p>\n

1. Section<\/b>\u00a0<\/b>formula:\u00a0<\/b><\/h3>\n

Let \u2018P\u2019 (x,y) be an internal point dividing point \u2018A\u2019 with coordinates \\left(x_{1}, y_{1}\\right)<\/span><\/span>and point \u2018B\u2019 with coordinates \\left(x_{2}, y_{2}\\right)<\/span><\/span>in the ratio m:n, then the coordinates of P is given by,<\/span><\/p>\n

<\/span><\/p>\n

\"\"<\/span><\/p>\n

<\/span><\/p>\n

2. Distance between 2 points:<\/b><\/h3>\n

The distance between two points ‘A’ with coordinates \\left(x_{1}, y_{1}\\right)<\/span><\/span>and point \u2018B\u2019 with coordinates \\left(x_{2}, y_{2}\\right)<\/span><\/span>is given by,<\/span><\/p>\n

<\/span><\/p>\n

\"\"<\/span><\/p>\n

<\/span><\/p>\n

3. The centroid of a triangle:<\/b><\/h3>\n

Let \u0394ABC be a triangle with vertices A\\left(x_{1}, y_{1}\\right), B\\left(x_{2}, y_{2}\\right) \\text {, and } C\\left(x_{3}, y_{3}\\right)<\/span><\/span>then the centroid of the triangle is given by,<\/span><\/p>\n

<\/span><\/p>\n

\"\"<\/span><\/p>\n

<\/span><\/p>\n

Solved Examples:<\/b><\/h2>\n

Q1) What is the centroid of a triangle with vertices A (1, 3), B(2, 2), and C(3, 1)?<\/b><\/p>\n

Ans:<\/strong> The centroid of a triangle with vertices A (1, 3), B(2, 2), and C(3, 1) is:<\/span><\/p>\n

X = (1+2+3)\/3 = 2<\/span><\/p>\n

Y = (3+2+1)\/3 = 2<\/span><\/p>\n

So the coordinate of centroid is (2,2).<\/span><\/p>\n

<\/span><\/p>\n

Q2) What is the distance between points A (8, 8) and B (5, 4)?<\/b><\/p>\n

Ans:<\/strong> The distance between the points A (8, 8) and B (5, 4) is:<\/span><\/p>\n

D=\\sqrt{\\left[(8-5)^{2}-(8-4)\\right]^{2}}=\\sqrt{25}=5 \\text { units }<\/span><\/span><\/p>\n

<\/span><\/p>\n

Q3) What is the coordinate of point C dividing the points A(1,1) and B(3,3) in the ratio 1:1 on a coordinate plane?<\/b><\/p>\n

Ans:\u00a0The coordinate of point C dividing the points A(1,1) and B(3,3) in the ratio 1:1 on a coordinate plane is:\u00a0 <\/span><\/b><\/p>\n

x=\\frac{(1 \\times 1)+(1 \\times 3)}{2}=2 \\text { and } y=\\frac{(1 \\times 1)+(1 \\times 3)}{2}=2<\/span><\/b><\/p>\n

So the coordinates of C are (2,2) on the coordinate plane.<\/span><\/p>\n

<\/span><\/p>\n

Uses of Coordinate Geometry<\/b><\/b><\/h2>\n
    \n
  1. Coordinate geometry used in navigation devices.<\/span><\/li>\n
  2. It is used in various editing software for drawing different kinds of shapes and edits.<\/span><\/li>\n
  3. Pixels of a photo position themselves using coordinate geometry in the camera.<\/span><\/li>\n
  4. It is used in drawing bar graphs, histograms, etc.<\/span><\/li>\n<\/ol>\n

    <\/span><\/p>\n

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    Explore Other Topics<\/h1>\n

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    \n
    Geometry<\/a><\/div>\n
    Trigonometry<\/a><\/div>\n
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    Numbers<\/a><\/div>\n<\/div>\n

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    Frequently Asked Questions\u00a0<\/span><\/span><\/h1>\n
      <\/ol>\n

      Q1. What is abscissa in coordinate geometry?
      <\/strong><\/h3>\n

      Ans: <\/strong>Abscissa in coordinate geometry refers to the x coordinate of the point.
      <\/strong><\/span><\/span><\/p>\n

      Q2. What is ordinates in coordinate geometry?
      <\/strong><\/h3>\n

      Ans: <\/strong>Ordinate refers to the Y coordinate of a point.<\/strong><\/p>\n

      Q3. What is the distance between points A\\left(x_{1}, y_{1}\\right) \\text { and } B\\left(x_{2}, y_{2}\\right) ?<\/span><\/b><\/strong><\/h3>\n

      Ans: <\/strong>The distance between two points ‘A’ with coordinates \\left(x_{1}, y_{1}\\right)<\/span><\/span>and point \u2018B\u2019 with coordinates \\left(x_{2}, y_{2}\\right)<\/span><\/span> is given by <\/span><\/p>\n

      D=\\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}}<\/span><\/span><\/p>\n

      <\/span><\/p>\n

      Q4. <\/strong>What is the coordinate of point C dividing the points<\/b>A\\left(x_{1}, y_{1}\\right) \\text { and } B\\left(x_{2}, y_{2}\\right) <\/span> <\/b><\/strong><\/b>in the ratio m:n on a coordinate plane?<\/b><\/h3>\n

      Ans: <\/b>\u00a0The coordinate of point C dividing the points A\\left(x_{1}, y_{1}\\right) \\text { and } B\\left(x_{2}, y_{2}\\right) <\/span> <\/span>in the ratio m:n on a coordinate plane is (x, y)=\\left(\\frac{m x_{2}+n x_{1}}{m+n}, \\frac{m y_{2}+n y_{1}}{m+n}\\right)<\/span>.<\/span><\/p>\n

      [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

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