Points in the coordinate system
Two points in a coordinate system: how far apart are they, where is the middle, and which line goes through both?
Your numbers
Answer
Distance between the points
10
Midpoint
(1 ; 4)
The line through the points
y = 0.75x + 3.25
How to work it out
- 1Δx = 5 − -3 = 8 · Δy = 7 − 1 = 6
- 2|AB| = √(Δx² + Δy²) = √(64 + 36) = 10
- 3M = ((-3 + 5) / 2 ; (1 + 7) / 2) = (1 ; 4)
- 4a = Δy / Δx = 6 / 8 = 0.75 · b = y₁ − a·x₁ = 3.25
The formula
|AB| = √((x₂ − x₁)² + (y₂ − y₁)²)
The distance formula is Pythagoras: Δx and Δy are the legs.
M = ((x₁ + x₂)/2 ; (y₁ + y₂)/2)
The midpoint is the average of the coordinates.
More: Geometry
- PythagorasFind the missing side of a right triangle — with a drawing and working.
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- The circleRadius, diameter, circumference and area from one known measurement — and sectors.
- Right triangleSine, cosine and tangent: all sides and angles from two known values.
- AnglesThe third angle in a triangle and the angle sum of a polygon.