Coordinate Geometry Formula Equations and Concept

Coordinate Geometry Formula : Coordinates serve as essential markers on our planet, allowing us to easily pinpoint locations on the world map. The Earth's coordinate system comprises imaginary lines known as latitudes and longitudes. Starting points for this system are the zero degrees 'Greenwich Longitude' and the zero degrees 'Equator Latitude.' In a similar manner, when locating a point on a plane or a piece of paper, we utilize coordinate axes consisting of the horizontal x-axis and the vertical y-axis.

Introduction to Coordinate Geometry

The Coordinate Plane

• The origin O, positioned at the intersection of the x-axis and y-axis, has coordinates (0, 0).
• To the right of the origin O, the x-axis is positive, and to the left, it is negative. Similarly, above the origin O, the y-axis is positive, while below it is negative.
• A point in the first quadrant (x, y) possesses positive values for both x and y and is situated relative to the positive x-axis and y-axis.
• In the second quadrant, a point (-x, y) is positioned with respect to the negative x-axis and positive y-axis.
• The third quadrant features a point (-x, -y), plotted relative to the negative x-axis and negative y-axis.
• The fourth quadrant hosts a point (x, -y), situated relative to the positive x-axis and negative y-axis.

Understanding the Coordinates of a Point

• Introduction to the coordinate plane and related terms.
• Understanding point coordinates and their representation across different quadrants.
• Formulas for calculating the distance between two points on the coordinate plane.
• Formulas for determining the slope of a line connecting two points.
• The midpoint formula for locating the midpoint of a line segment.
• The section formula for finding points that divide a line segment in a specific ratio.
• Determining the centroid of a triangle using its vertices on the coordinate plane.
• Calculating the area of a triangle with vertices in the coordinate geometry plane.
• Exploring the equation of a line and its various forms.

Also Check - Linear Equation Formula

Coordinate Geometry Formulas

Coordinate Geometry Distance Formula

Also Check - Algebra Formulas

Coordinate Geometry Slope Formula

Finding Slope from a Graph

• Step 1: Note the coordinates of the two points lying on the line, (x 2 , y 2 ), (x 1 , y 1 ). Here the coordinates are given as (2, 4), (1, 2).
• Step 2: Apply the slope of line formula, m = (y 2 - y 1 )/(x 2 - x 1 ) = (4 - 2)/(2 - 1) = 2.
• Step 3: Therefore, the slope of the given line = 2.

Coordinate Geometry Mid-Point Formula

Coordinate Geometry Section Formula

Coordinate Geometry Centroid Formula

Coordinate Geometry Area of a Triangle Formula

Determining the Equation of a Line in Coordinate Geometry

Points to Remember About Cartesian Coordinates

• The slope of the x-axis holds a value of 0, while the slope of the y-axis is considered infinite (∞).
• The x-axis is represented by the equation y = 0, and the y-axis is described by the equation x = 0.
• A point situated on the x-axis takes the form (a, 0), whereas a point located on the y-axis is represented as (0, b).
• The equation of a line in slope-intercept form is y = mx + c.
• In the coordinate plane, two lines that are parallel possess equal slopes.
• Furthermore, in the coordinate plane, when considering two perpendicular lines, the product of their slopes is equivalent to -1.