Coordinate Geometry Concepts

Understanding the Concepts of Coordinate Geometry

Coordinate geometry is the study of geometric figures using coordinate axes. Straight lines, curves, circles, ellipses, hyperbolas, and polygons can all be conveniently drawn and scaled in the coordinate axes.

Advanced coordinate geometry allows you to work algebraically and examine the characteristics of geometric figures using the coordinate system.

A clear visualisation of the 2D graph and a comprehension of the coordinates will assist us to answer problems faster. Coordinate geometry problems in aptitude concentrate primarily with coordinates in the x-y axis.

The diagram below will help you understand it better.

You can now understand the fundamental concepts of Coordinate Geometry. Listed below are the different Coordinate Geometry concepts:

1. Coordinate Plane
2. Coordinates of a Point
3. Coordinate Geometry Distance calculation ( Two Point formula)
4. Slope
5. Mid-point
6. Section Formula in Coordinate Geometry
7. The centroid of a Triangle
8. Area of a Triangle Coordinate Geometry Formula
9. Finding the Equation of a Line in Coordinate Geometry

1. Coordinate Plane

A cartesian plane divides plane space into two dimensions and is useful for locating points. It's also known as the coordinate plane.

The coordinate plane has two axes: the horizontal x-axis and the vertical y-axis.

These coordinate axes divide the plane into four quadrants, and the point of intersection of these axes is the origin (0, 0).

Furthermore, each point in the coordinate plane is represented by a point (x, y), where

• The x value is the position of the point with reference to the x-axis, and
• The y value is the position of the point with reference to the y-axis.

2. Coordinates of a Point

A coordinate is an address that helps in the positioning of a point in space. The coordinates of a point in a two-dimensional space are (x, y).

3. Coordinate Geometry Distance Calculation (Two Point formula)

The distance between two points (x1, y1) and (x2, y2) is equal to the square root of the sum of the squares of the difference of the two provided points' x and y coordinates.

The following is the formula for calculating the distance between two locations.

D = √(x2−x1)2+ (y2−Y1)2

4. Slope

The inclination of a line is represented by its slope. The slope can be calculated by selecting any two points on the line or by calculating the angle formed by the line with the positive x-axis.

The slope of a line inclined at an angle θ with the positive x-axis is m = Tanθ.

The slope of a line joining the two points (x1, y1)and (x2,y2) n is equal to m = (y2−y1)/(x2−x1)

m = Tanθ

m = (y2−y1)/(x2−x1)

5. Mid-point

The formula for finding the midpoint of the line connecting the points (x1, y1) and (x2, y2) yields a new point with an abscissa equivalent to the average of the x values of the two provided points and an ordinate equal to the average of the y values of the two given points.

The midpoint is positioned exactly between the two locations on the line connecting them.

(x,y)=[(x1+x2)/2 ,(y1+y2)/2]

6. Section Formula in Coordinate Geometry

The section formula can be used to get the coordinates of a point that divides the line segment connecting the points (x1, y1) and (x2,y2) in the ratio m:n.

The point dividing the provided two points is located on the line connecting the two points and can be found either between the two points or outside the line segment between the points.

(x,y)=[(mx2+nx1)/(m+n),(my2+ny1)/(m+n)]

7. The centroid of a Triangle

A triangle's centroid is the point at which its medians connect. (A median is a line that connects a triangle's vertex to the midpoint of the opposing side.)

The following formula yields the centroid of a triangle with vertices A(x1,y1), B(x2,y2), and C(x3,y3).

(x,y)=[(x1+x2+x3)/3,(y1+y2+y3)/3)]

8. Area of a Triangle Coordinate Geometry Formula

The following formula calculates the area of a triangle with the vertices A (x1,y1), B (x2,y2), and C (x3,y3).

This triangle area formula is applicable to all forms of triangles.

Area of a Triangle = 1/2|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|

9. Finding the Equation of a Line in Coordinate Geometry

With the use of a basic linear equation, this line equation depicts all of the points on the line. The standard form of the equation of a line is ax + by + c= 0.

There are several methods for determining a line's equation. The slope-intercept form of the equation of a line (y = mx + c) is another integral part of the equation of a line.

y = mx + c

Here

m is the slope of the line

c is the y-intercept of the line.