| 1. | Distance Formula: Distance(d) between two points A(x1, y1) and B(x2, y2) is given by
| ||||||||||
| 2. | Section Formula: Coordinate of a point P(x, y) which divides the line joining two points (x1, y1) and (x2, y2) in the ratio of m:n internally and externally are given by
| ||||||||||
| 3. | Mid-Point Formula: Mid-point P(x, y) of the line joining two points (x1, y1) and (x2, y2) is given by
| ||||||||||
| 4. | Centroid of a Triangle: Centroid P(x, y) of a triangle with vertices (x1, y1), (x2, y2) and (x3, y3) is given by
| ||||||||||
| 5. | Slope of a Line Formula:
a. Slope of a straight line which makes angle θ with x-axis in positive direction is given by Slope(m) = tanθ b. Slope of a straight line passing through the points (x1, y1) and (x2, y2) is given by
| ||||||||||
| 6. | Slope Intercept Form: Equation of a straight line with slope m and y-intercept c is given by y = mx + c | ||||||||||
| 7. | Double Intercept Form: Equation of a traight line with x-intercept a and y-intercept b is given by
| ||||||||||
| 8. | Normal Form: Equation of a straight line with perpendicular from origin p and angle of perpendicular with x-axis α is given by xcosα + ysinα = p | ||||||||||
| 9. | Point Slope Form: Equation of a straight line with m and passing through the point (x1, y1) is given by y – y1 = m(x – x1) | ||||||||||
| 10. | Two Points Form: Equation of a straight line passing through the points (x1, y1) and (x2, y2) is given by
| ||||||||||
| 11. | Perpenducular Distance: a. Perpendicular distance(d) from the point (x1, y1) to the line xcosα + ysinα = p is given by d = ±(x1cosα + y1sinα – p) b. Perpendicular distance(d) from the point (x1, y1) to the line Ax + By + C = 0 is given by
| ||||||||||
| 12. | Area of Triangle: Area of triangle with vertices (x1, y1), (x2, y2) and (x3, y3) is given by
| ||||||||||
| 13. | Area of Quadrilateral: Area of quadrilateral with vertices (x1, y1), (x2, y2), (x3, y3) and (x4, y4) is given by
| ||||||||||
| 14. | Angle Between Two Straight Lines: Angle between two straight lines with slope m1 and m2 is given by
Cor2: when m1×m2 = -1, the lines are perpendicular. | ||||||||||
| 15. | Equation of a Circle: a. Equation of a circle with center at origin O(0, 0) and radius r is given by x2 + y2 = r2 b. Equation of a circle with center at any point (h, k) and radius r is given by x2 + y2 +2gx + 2fy + c = 0 Where where, g = -h, f = -k, and c = h2 + k2 + r2 | ||||||||||
| 16. | Equation of a Circle in Diameter Form:
Equation of a circle with two end points of a diameter (x1, y1) and (x2, y2) is given by (x – x1)(x – x2) + (y – y1)(y – y2) = 0 |
Coordinate geometry, also known as analytic geometry, bridges the gap between algebra and geometry by using a coordinate system to represent points and geometric figures on a plane. Mastering the formulas of coordinate geometry is fundamental for understanding and solving a wide range of mathematical problems. This comprehensive guide provides a clear and concise overview of essential coordinate geometry formulas, empowering you to navigate the plane with confidence.
Understanding the Coordinate Plane: Axes and Points
Before diving into the formulas, let's recap the basics of the coordinate plane:
Essential Coordinate Geometry Formulas:
Here's a breakdown of the key formulas you'll need:
Distance Formula: Calculates the distance between two points (x₁, y₁) and (x₂, y₂).
Midpoint Formula: Calculates the coordinates of the midpoint of a line segment joining two points (x₁, y₁) and (x₂, y₂).
Slope Formula: Calculates the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂). The slope represents the steepness of the line.
Equations of a Line:
There are several forms for the equation of a straight line:
Illustrative Examples: Putting Formulas into Practice
Let's work through some examples to understand how to apply these formulas:
Example 1: Find the distance between the points (2, 3) and (5, 7).
Example 2: Find the midpoint of the line segment joining the points (1, 4) and (7, 2).
Example 3: Find the slope of the line passing through the points (2, 5) and (6, 13).
Example 4: Find the equation of the line with a slope of 3 and passing through the point (4, -1) using the point-slope form.
Example 5: Find the equation of the line passing through the points (2, 3) and (5, 7) using the two-point form.
Why This Article Matters:
This article is optimized for search engines using relevant keywords such as "coordinate geometry," "coordinate geometry formulas," "coordinate geometry formula," "distance formula," "midpoint formula," "slope formula," "equation of a line," "slope-intercept form," "point-slope form," and "two-point form." This ensures that when you search for information on coordinate geometry, this page is more likely to appear in the search results.
Applications of Coordinate Geometry:
Coordinate geometry has applications in various fields, including:
Conclusion: Mastering Coordinate Geometry
Understanding coordinate geometry is essential for solving a wide range of mathematical problems and has practical applications in many fields. This guide provides a valuable resource for learning and applying these fundamental formulas. By mastering these concepts, you'll be better equipped to tackle challenges in mathematics, science, engineering, and various real-world applications.
Call to Action:
Bookmark this page for quick reference and share it with others who might find it helpful. Practice applying these formulas to different coordinate geometry problems to reinforce your understanding. Visualizing points and lines on the coordinate plane will solidify your grasp of these concepts.