Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Important Formulas: Coordinate Geometry
Important Formulas: Coordinate Geometry | Mathematics (Maths) Class 9 PDF Download
Introduction
Coordinate geometry plays a vital role in mathematics by visually representing geometric shapes in a two-dimensional plane and enhancing understanding of their inherent properties. In this exploration, we delve into the coordinate plane and the concept of point coordinates, aiming to provide an introductory understanding of the realm of coordinate geometry.
Coordinate Plane
The Cartesian plane, or coordinate plane, divides the plane into two dimensions using the horizontal x-axis and the vertical y-axis. This system allows precise location identification, with the intersection point termed the origin (0, 0). Points on the coordinate plane are represented as (x, y), where 'x' denotes the position relative to the x-axis, and 'y' indicates the position concerning the y-axis. The plane is further divided into four quadrants by these axes.
Locating points on the graph
- We require two perpendicular axes to locate a point in the plane. One of them is horizontal and other is Vertical
- The plane is called the Cartesian plane and axis are called the coordinates axis
- The horizontal axis is called x-axis and vertical axis is called Y-axis
- The point of intersection of axis is called origin.
- The distance of a point from y-axis is called x-coordinate or abscissa and the distance of the point from x-axis is called y-coordinate or Ordinate
- The distance of a point from the axis is called x-coordinate or abscissa and the distance of the point from x-axis is called y-coordinate or Ordinate
- The Origin has zero distance from both x-axis and y-axis so that its abscissa and ordinate both are zero. So the coordinate of the origin is (0, 0)
- A point on the x–axis has zero distance from x-axis so coordinate of any point on the x-axis will be (x, 0)
- A point on the y–axis has zero distance from y-axis so coordinate of any point on the y-axis will be (0, y)
- The axes divide the Cartesian plane into four parts. These Four parts are called the quadrants
The coordinates of the points in the four quadrants will have signs according to the below table
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FAQs on Important Formulas: Coordinate Geometry - Mathematics (Maths) Class 9
| 1. What is the Coordinate Plane and how is it structured? |  |
Ans.The Coordinate Plane is a two-dimensional surface defined by a horizontal axis (x-axis) and a vertical axis (y-axis). The point where these axes intersect is called the origin, denoted as (0,0). The plane is divided into four quadrants: Quadrant I (x > 0, y > 0), Quadrant II (x < 0, y > 0), Quadrant III (x < 0, y < 0), and Quadrant IV (x > 0, y < 0). Each point in this plane can be represented by an ordered pair (x, y).
| 2. How do you calculate the distance between two points in the Coordinate Plane? | |
Ans.The distance between two points, say (x₁, y₁) and (x₂, y₂), can be calculated using the Distance Formula:
\[ d = \sqrt{(x₂ - x₁)² + (y₂ - y₁)²} \]
This formula derives from the Pythagorean theorem and helps in finding the straight-line distance between the two points.
| 3. What is the Slope Formula and why is it important? | |
Ans.The Slope Formula is used to determine the steepness or inclination of a line that passes through two points (x₁, y₁) and (x₂, y₂). The formula is given by:
\[ m = \frac{(y₂ - y₁)}{(x₂ - x₁)} \]
where \( m \) represents the slope. Understanding the slope is crucial for analyzing linear relationships between variables in coordinate geometry.
| 4. How can the Midpoint Formula be used in coordinate geometry? | |
Ans.The Midpoint Formula is used to find the exact center point between two coordinates (x₁, y₁) and (x₂, y₂). The formula is:
\[ M = \left( \frac{x₁ + x₂}{2}, \frac{y₁ + y₂}{2} \right) \]
This formula is particularly useful in dividing segments into two equal parts and in various geometric constructions.
| 5. What is the formula for the area of a triangle in Coordinate Geometry? | |
Ans.The area of a triangle formed by three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) in the coordinate plane can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) | \]
This formula helps in finding the area without needing to determine the height or base directly, making it very useful for various applications in coordinate geometry.
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