Coordinate geometry is based on the Cartesian coordinate system, which was developed by René Descartes. It consists of two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), which intersect at the origin (0,0)
Requirements:
1. Cartesian Coordinate System:
Coordinate geometry is based on the Cartesian coordinate system, which was developed by René Descartes. It consists of two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), which intersect at the origin (0,0).
2. Points in the Plane:
A point in the plane is represented by an ordered pair of numbers (x, y), where x is the horizontal distance from the origin along the x-axis, and y is the vertical distance from the origin along the y-axis.
3. Distance Formula:
The distance between two points, (x₁, y₁) and (x₂, y₂), in a Cartesian coordinate system is given by the distance formula:
Distance = √((x₂ – x₁)² + (y₂ – y₁)²)
4. Midpoint Formula:
The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the midpoint formula:
Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
5. Slope of a Line:
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ – y₁) / (x₂ – x₁)
6. Equation of a Line:
The equation of a line in slope-intercept form is given by:
y = mx + b
where m is the slope, and b is the y-intercept (the point where the line crosses the y-axis).
7. Parallel and Perpendicular Lines:
Two lines are parallel if they have the same slope.
Two lines are perpendicular if the product of their slopes is -1.
8. Linear Equations:
A linear equation is an equation that represents a straight line on a coordinate plane. It can be written in the form Ax + By = C, where A, B, and C are constants.
9. Quadratic Equations:
Quadratic equations represent parabolic curves on a coordinate plane. They are typically written in the form Ax² + Bx + C = 0, where A, B, and C are constants.
10. Conic Sections:
– Coordinate geometry also deals with conic sections, which are curves formed by the intersection of a plane and a cone. The main types of conic sections are circles, ellipses, parabolas, and hyperbolas.
11. Analytic Geometry:
– Analytic geometry extends the principles of coordinate geometry to three-dimensional space, where points are represented by ordered triples (x, y, z).
12. Applications:
– Coordinate geometry is widely used in various fields, including physics, engineering, computer graphics, and geography, for solving problems related to measurement, navigation, and modeling.
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