Coordinate Geometry
Distance formula, midpoint formula, and equations of lines
Start with the basics and progress through 3 lessons. Each lesson builds on the previous one.
0 of 3 lessons done
In This Topic (3 lessons)
The Distance Formula
Learn how to calculate the distance between two points on a coordinate plane using the distance formula.
Coordinate Geometry Proofs
Learn how to prove geometric properties using coordinates, algebraic formulas, and logical reasoning.
Equations of Lines in Coordinate Geometry
Learn how to write and interpret equations of lines using slope-intercept, point-slope, and standard forms.
Coordinate geometry combines algebra and geometry, allowing geometric problems to be solved using equations. By placing shapes on a coordinate plane, we can calculate distances, slopes, midpoints, and determine relationships between lines and shapes using algebraic formulas. This powerful approach opens doors to advanced mathematics and real-world applications.
What You'll Learn
- Calculate distance between points using the distance formula
- Find midpoints of line segments
- Determine slopes of lines
- Write equations of lines given points or slopes
- Apply coordinate geometry to geometric proofs
Frequently Asked Questions
What is the distance formula?
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$, derived from the Pythagorean theorem applied to the horizontal and vertical distances between two points.
How do I find the equation of a line?
Use point-slope form $y - y_1 = m(x - x_1)$ with a point and slope, or slope-intercept form $y = mx + b$ with slope and y-intercept.
What makes lines parallel or perpendicular?
Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals (their product equals -1).