Interactive — Coordinate Geometry

x = 3 y = 2

Drag the sliders to move the point (x, y). Watch which quadrant it lands in and how the abscissa & ordinate change sign.

Drag either point on the grid

Distance Formula: PQ = √[(x₂−x₁)² + (y₂−y₁)²]. The dashed legs form a right triangle — the distance is its hypotenuse (Pythagoras).

m = 1 n = 1

Section Formula: the point P divides AB internally in the ratio m : n. Change m and n to slide P along the segment.

Drag either endpoint

Midpoint: M = ( (x₁+x₂)/2 , (y₁+y₂)/2 ) — simply the average of the coordinates. It always sits exactly halfway.

Drag any of the three vertices

Area = ½|x₁(y₂−y₃)+x₂(y₃−y₁)+x₃(y₁−y₂)|. Line the vertices up and watch the area shrink to 0 — that is the collinearity test!

GPS positions are coordinates. The distance formula gives the straight-line distance between two locations.

Every pixel on a screen has (x, y) coordinates. Midpoints and sections place objects precisely.

The area formula finds a plot's area directly from the coordinates of its corners.

Robot arms plan paths by dividing segments in ratios — exactly the section formula.

Collision checks use distances; sprite centres use midpoints and centroids.

Checking if three waypoints are collinear (area = 0) keeps aircraft on a straight route.

Coordinate geometry turns geometry into algebra — every shape becomes a set of equations you can calculate with.