Distance and Midpoints

Explanation

Analytic Geometry uses the coordinate plane to study geometry.

1. Distance formula: The distance between two points (x1,y1) and (x2,y2) is

d= sqrt{(x2 – x1)^2 + (y2 – y1)^2}​

2. Midpoint formula: The midpoint of a segment connecting (x1,y1) and (x2,y2) is

M=({x1+x2}/{2}}, {y1+y2}/{2})

Example: Points (2,3) and (6,7)

• Distance: d = sqrt{(6-2)^2 + (7-3)^2} = sqrt{16+16} = sqrt{32} = 4sqrt{2}​

• Midpoint: M = ( {2+6}/{2}, {3+7}/{2} ) = (4, 5)