Coordinate Geometry is the study of geometric figures using a coordinate plane. It connects algebra and geometry by using equations to represent shapes.
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
The slope of a line through two points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Find the distance between (3, 4) and (7, 1)
d = √[(7 - 3)² + (1 - 4)²]
= √[16 + 9]
= √25
= 5