{"id":6819,"date":"2021-12-27T07:45:58","date_gmt":"2021-12-27T07:45:58","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6819"},"modified":"2021-12-27T18:38:32","modified_gmt":"2021-12-27T18:38:32","slug":"coordinate-geometry-formulas-concept-examples-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/coordinate-geometry-formulas-concept-examples-and-faqs\/","title":{"rendered":"Coordinate Geometry Formulas: Concept, Examples and FAQs"},"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 Formulas: Concept, Examples and FAQs<\/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 Formulas<\/b><\/h2>\n

The coordinate geometry formulas include distance formula, slope formula, midpoint formula, the angle between lines formula, section formula, and the equation of a line formula.\u00a0<\/span><\/b><\/p>\n

Before learning about these formulas, let us have a look at the concept of coordinate geometry.<\/span><\/p>\n

 <\/p>\n

What Is Coordinate Geometry?<\/b><\/h2>\n

Coordinate geometry is a representation of geometric forms on a two-dimensional plane. Before coming to formulas, we will understand the concept of a coordinate plane and the coordinates of a point.<\/span><\/p>\n

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

Coordinate Plane<\/b><\/b><\/h3>\n

The cartesian plane consists of 2 number lines, x-Axis (Horizontal) and y-Axis (Vertical), perpendicular to each other. It is known as a coordinate plane. These x and y axes divide the cartesian plane into four quadrants, and the point of intersection of these two lines is the origin.\u00a0<\/span><\/p>\n

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

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

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

Any random point on the coordinate plane is represented by a point (x, y), where the x value is the distance of the point from the x-axis, and the y value is the distance of the point from the y-axis.<\/span><\/span><\/p>\n

The coordinates of origin O are (0, 0).<\/span><\/span><\/p>\n

Any point represented in the first quadrant has both positive values, and its coordinates are in the form of (x, y).<\/span><\/span><\/p>\n

Points represented in the second, third, and fourth quadrant have coordinates of the form (-x, y), (-x, -y), and (x, -y) respectively.<\/span><\/p>\n

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

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

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

If two points A and B coordinates are \\left(x_{1}, y_{1}\\right) \\text { and }\\left(x_{2}, y_{2}\\right)<\/span><\/span>, then the distance between these points is given as<\/span><\/p>\n

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

<\/b><\/h2>\n

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

The slope of a line is the ratio of vertical change or inclination of the line. The slope of a line inclined at an angle \u03b8 with the positive x-axis is given by m = tan \u03b8.\u00a0<\/span><\/p>\n

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

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

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

The formula for the slope of a line joining the two points A\\left(x_{1}, y_{1}\\right) \\text { and } B\\left(x_{2}, y_{2}\\right)<\/span><\/span>is<\/span><\/p>\n

m=\\frac{\\left(y_{2}-y_{1}\\right)}{\\left(x_{2}-x_{1}\\right)}<\/span><\/span><\/p>\n

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

Mid-Point Formula<\/b><\/h2>\n

For finding the coordinates of the mid-point of the line joining the points<\/span>\u00a0\\left(x_{1}, y_{1}\\right) \\text { and }\\left(x_{2}, y_{2}\\right)<\/span>we use the formula<\/span><\/p>\n

(x, y)=\\left(\\frac{x_{1}+x_{2}}{2},\\frac{y_{1}+y_{2}}{2}\\right)<\/span><\/span><\/p>\n

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

Section Formula: Coordinates of The Point Which Divides a Line into m:n Ratio<\/b><\/h2>\n

The section formula in coordinate geometry represents the coordinates of the point that divides a line segment joining 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. We can find the coordinates of the point using the formula given below.<\/span><\/p>\n

(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

 <\/p>\n

Area of a Triangle Formula in a Coordinate Plain<\/b><\/h2>\n

The area of a triangle in a cartesian plane whose vertices are \\left(x_{1}, y_{1}\\right),\\left(x_{2}, y_{2}\\right), \\text { and }\\left(x_{3}, y_{3}\\right)<\/span> <\/span>is given by the formula.\u00a0<\/span><\/p>\n

\\text { Area of the triangle }=\\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|<\/span><\/span><\/p>\n

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

The Angle Between Two Lines Formula:<\/b><\/h2>\n

Consider two straight lines A and B, having slopes m_1\\text{ and }m_2<\/span><\/span>,<\/span> respectively.<\/span><\/p>\n

If the angle between these lines is \u2018\u03b8\u2019, then the angle between them can be calculated using the formula<\/span><\/p>\n

\\tan \\theta=\\frac{\\left(m_{1}-m_{2}\\right)}{\\left(1+m_{1} m_{2}\\right)}<\/span><\/span><\/p>\n

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

Equation of a Line Formula in a Cartesian Plane<\/b><\/h2>\n

The equation of a line in a coordinate plane can be expressed in different ways. Some of them are given below.<\/span><\/p>\n

(i) General Form<\/b><\/h3>\n

The general form of a line in a cartesian plane is represented by <\/span>Ax + By + C = 0.<\/b><\/p>\n

(ii) Slope intercept Form\u00a0<\/b><\/h3>\n

Let a line passes through a point whose coordinates are (x, y), \u2018m\u2019 be the slope of the line, and \u2018c\u2019 be the y-intercept, then the equation of a line formula is given by:<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/span>\u00a0y = mx + c<\/b><\/p>\n

 <\/p>\n

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

<\/b><\/p>\n

1. Find the distance between two points P (4,5) and Q (-3,8)?
<\/b><\/p>\n

Ans: <\/b>We know that the coordinate geometry distance formula 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

\\text { Here } x_{1}=4, y_{1}=5, x_{2}=-3, y_{2}=8<\/span><\/span><\/p>\n

d =\\sqrt{(-3-4)^{2}+(8-5)^{2}} <\/span>
=\\sqrt{(-7)^{2}+(3)^{2}} <\/span>
=\\sqrt{49+9} <\/span>
=\\sqrt{58}<\/span><\/span><\/p>\n

Therefore, the distance between points is \u221a58 units.<\/span><\/p>\n

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

2. What is the equation of a line having a slope of (-4) and y-intercept of 3?<\/strong><\/p>\n

Ans:<\/strong><\/p>\n

Given,
Slope (m) = -4 and
y-intercept (c) = 3
Equation of slope intercept form of the line is given by the formula
y = mx + c
y = (-4)x + 3
y = -4x + 3
4x + y = 3
Therefore, the equation of the line is 4x + y = 3<\/span><\/p>\n

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Explore Other Topics<\/h1>\n

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

[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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Related Concepts<\/h1>\n

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\n
Prime numbers from 1 to 100<\/a><\/div>\n
53 prime or composite?<\/a><\/div>\n
Is 73 a prime number?<\/a><\/div>\n<\/div>\n

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

    Q1. What is the section formula in cartesian geometry?
    <\/strong><\/h3>\n

    Ans: <\/strong>The section formula in coordinate geometry represents the coordinates of the point that divides a line into an m:n ratio. We can find the coordinates of this point using the formula given below.
    (x, y)=\\left(\\frac{m x_{2}+n x_{1}}{m+n},\\frac{m y_{2}+n y_{1}}{m+n}\\right)<\/span><\/span><\/span><\/span><\/p>\n

    Q2. What is the distance formula in cartesian geometry?
    <\/strong><\/h3>\n

    Ans: <\/strong>The distance formula in cartesian geometry is useful for finding the distance between two points in the coordinate plane. If two points A and B coordinates are \\left(\\left(x_{1}, y_{1}\\right) \\text { and }\\left(x_{2}, y_{2}\\right)\\right.<\/span> then the distance between these points is given as d=\\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}}<\/span><\/strong><\/p>\n

    Q3. What is the slope formula in cartesian geometry?<\/strong><\/h3>\n

    Ans:\u00a0 <\/strong>The slope of a line is the ratio of vertical change or inclination of the line. The slope of a line inclined at an angle \u03b8 with the positive x-axis is given by m = tan \u03b8. The formula for the slope of a line joining the points \\mathrm{A}\\left(\\mathrm{x}_{1}, \\mathrm{y}_{1}\\right) \\text { and } \\mathrm{B}\\left(\\mathrm{x}_{2}, \\mathrm{y}_{2}\\right)<\/span><\/span>is given by \\mathrm{m}=\\frac{\\mathrm{y}_{2}-\\mathrm{y}_{1}}{\\mathrm{x}_{2}-\\mathrm{x}_{1}}<\/span><\/span><\/p>\n

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    Meta Description: We can calculate the sum of the terms in a geometric progression using the formula S = a(1-r^n)\/(1-r) when r < 1 and S = a(r^n-1)\/(r-1)when r>1<\/p>\n","protected":false},"author":10,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"\nCoordinate Geometry Formulas: Concept, Examples and FAQs - mydomain<\/title>\n<meta name=\"description\" content=\"Meta Description: We can calculate the sum of the terms in a geometric progression using the formula S = a(1-r^n)\/(1-r) when r < 1 and S = a(r^n-1)\/(r-1)when r>1\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/coordinate-geometry-formulas-concept-examples-and-faqs\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Coordinate Geometry Formulas: Concept, Examples and FAQs - 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