Coordinate Geometry

5 minQuiz at the end

The Coordinate Plane

The coordinate plane has two axes:

  • x-axis β€” horizontal
  • y-axis β€” vertical
  • Origin β€” (0, 0), where the axes meet

Points are written as (x, y).

The Four Quadrants

Quadrantxy
I++
IIβˆ’+
IIIβˆ’βˆ’
IV+βˆ’

Midpoint Formula

The midpoint between (x₁, y₁) and (xβ‚‚, yβ‚‚):

M = ((x₁+xβ‚‚)/2, (y₁+yβ‚‚)/2)

Midpoint of (2,4) and (8,10): ((2+8)/2, (4+10)/2) = (5, 7)

Distance Formula

Distance between (x₁, y₁) and (xβ‚‚, yβ‚‚):

d = √[(xβ‚‚-x₁)Β² + (yβ‚‚-y₁)Β²]

Distance from (0,0) to (3,4): √(9+16) = √25 = 5

(This is the Pythagorean theorem applied to coordinates!)

Gradient Formula

m = (yβ‚‚-y₁) / (xβ‚‚-x₁)

Gradient of (1,2) to (4,11): (11-2)/(4-1) = 9/3 = 3