Coordinate Geometry Basics

What is Coordinate Geometry?

• Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and their properties using algebraic and analytic methods.
• It involves the use of coordinates (x, y) to locate points in a plane and to define geometric shapes.

Coordinate Plane

• A coordinate plane is a two-dimensional plane formed by two perpendicular lines, the x-axis and the y-axis.
• The x-axis is the horizontal line, and the y-axis is the vertical line.
• The point of intersection of the two axes is called the origin (0, 0).

Quadrants

• The coordinate plane is divided into four quadrants:
  1. Quadrant I: x > 0, y > 0
  2. Quadrant II: x < 0, y > 0
  3. Quadrant III: x < 0, y < 0
  4. Quadrant IV: x > 0, y < 0

Distance Formula

• The distance between two points (x1, y1) and (x2, y2) is given by: √((x2 - x1)^2 + (y2 - y1)^2)

Midpoint Formula

• The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by: ((x1 + x2)/2, (y1 + y2)/2)

Slope Formula

• The slope of a line passing through two points (x1, y1) and (x2, y2) is given by: (y2 - y1) / (x2 - x1)

Equations of Lines

• The equation of a line can be written in various forms:
  • Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept
  • Point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope
  • Standard form: Ax + By = C, where A, B, and C are constants

Circles

• The equation of a circle with center (h, k) and radius r is given by: (x - h)^2 + (y - k)^2 = r^2

Coordinate Geometry

• Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and their properties using algebraic and analytic methods.
• It involves the use of coordinates (x, y) to locate points in a plane and to define geometric shapes.

Coordinate Plane

• A coordinate plane is a two-dimensional plane formed by two perpendicular lines, the x-axis and the y-axis.
• The x-axis is the horizontal line, and the y-axis is the vertical line.
• The point of intersection of the two axes is called the origin (0, 0).

Quadrants

• The coordinate plane is divided into four quadrants.
• Quadrant I: x > 0, y > 0
• Quadrant II: x < 0, y > 0
• Quadrant III: x < 0, y < 0
• Quadrant IV: x > 0, y < 0

Distance Formula

• The distance between two points (x1, y1) and (x2, y2) is given by: √((x2 - x1)^2 + (y2 - y1)^2)

Midpoint Formula

• The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by: ((x1 + x2)/2, (y1 + y2)/2)

Slope Formula

• The slope of a line passing through two points (x1, y1) and (x2, y2) is given by: (y2 - y1) / (x2 - x1)

Equations of Lines

• The equation of a line can be written in various forms.
• Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept
• Point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope
• Standard form: Ax + By = C, where A, B, and C are constants

Circles

• The equation of a circle with center (h, k) and radius r is given by: (x - h)^2 + (y - k)^2 = r^2