Math on the Grid.
Analyzing geometric shapes using algebraic equations on an x,y plane.
Before Descartes, Geometry was pictures and Algebra was equations. He married them, allowing us to prove geometric truths with calculation.
Distance = Pythagorean Theorem. Midpoint = Average of coordinates.
Plain English: Instead of drawing on blank paper, we draw on a map (grid). Every point has an address (x, y). We can calculate the distance between addresses without measuring tape.
Real-world example: Video Game Physics. Collision detection relies on calculating the distance between the player's center point and the enemy's center point.
Subtracting Negatives. In the distance formula (x2 - x1), if x1 is negative, it becomes a positive (minus a minus).