Coordinate geometry deals with the positions of points on a plane using their numerical coordinates.
To work with lines in coordinate geometry, you first need to understand the basics:
- The coordinate plane is divided into four quadrants.
- Every point on this plane is identified by an ordered pair (x, y).
- The x-value indicates the horizontal position, and the y-value indicates the vertical position.
Lines on this plane can be represented using equations like
y = mx + b, where
m is the slope and
b is the y-intercept.
Using coordinate geometry, we can calculate the distance between points, the slope of lines, and check if lines are parallel or perpendicular.
For instance, in our exercise, we used points (6, 9) and (2, 4) to find the line's slope and determined if it is parallel to the line with slope \( \frac{5}{4} \) that passes through (2, 1).