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:
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):
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:
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:
Nice explanation for someone like me who has just started learning coordinate geometry.