Concept 7.3
The Mid-point
Source: NCERT Mathematics, Class 106 minute lesson
Formal statement
The mid-point of the segment joining A(x₁, y₁) and B(x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2). It is the section formula with m = n = 1.
The intuition
The mid-point is the average of the two ends, coordinate by coordinate: halfway in x, halfway in y.
Half the difference, (x₂ − x₁)/2, is something else: it is how far you travel to get halfway, not where you arrive.
The attention
Look for the average: add the coordinates, then halve.
M = ( (x₁ + x₂)/2 , (y₁ + y₂)/2 ) not (x₂ − x₁)/2
Look hereNot here
- Look here
- The average of the coordinates. Averaging lands you exactly between the two ends.
- Not here
- Half the difference. Half the difference is a distance, not a position. It only equals the mid-point when one end is at 0.
- What it teaches
- Ask whether a quantity is a position or a distance. They live on different scales.