Basics of Coordinate Geometry: Slope, Line Equation, and Midpoint Explained

Coordinate geometry, also called Cartesian geometry, is a branch of mathematics that uses a grid with an X-axis and Y-axis to study shapes and points. Every point on this 2D plane (XY-plane) is represented by a pair of numbers, called a coordinate pair or 2-tuple: (x,y).

  • The first number, x, represents the point’s position along the X-axis (horizontal).
  • The second number, y, represents the point’s position along the Y-axis (vertical).

The X-axis (horizontal, left to right) and the Y-axis (vertical, up and down) divide the plane into four sections, called quadrants:

  • Quadrant I: x>0, y>0 (both positive)
  • Quadrant II: x<0, y>0 (negative x, positive y)
  • Quadrant III: x<0, y<0 (both negative)
  • Quadrant IV: x>0, y<0 (positive x, negative y)

In this video, I explain the fundamentals of coordinate geometry, covering topics such as the quadrant of given points, finding the equation of a line connecting two points, and determining the midpoint of a line segment. Here are some formulas that I discuss in the video:

Midpoint of a Line Segment

The midpoint of a line segment joining two points A(x1, y1) and B(x2, y2) is the point exactly halfway between them:

\( \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)
Slope of a Line

The slope of a line measures its steepness. For a line passing through two points A(x1, y1) and B(x2, y2):

\( \text{Slope} = \frac{y_2 – y_1}{x_2 – x_1} \)

Horizontal line: Slope = 0 and Vertical line: Slope = Undefined

Equation of a Line

If the slope of a line is m and it intersects the Y-axis at b (the y-intercept), the equation of the line:

\( y = mx + b \)

To test your understanding, there is a quiz available on this topic. You can find the link to the quiz below.

Links to the related quiz are here:

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