Separate distance from midpoint by using differences for length and averages for location.
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First lesson in this subject: Complete the angle sum
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Between A(1, 1) and B(5, 4), the horizontal change is 5 − 1 = 4 and the vertical change is 4 − 1 = 3. These are perpendicular legs of a right triangle.
The straight distance is √(4² + 3²) = 5. The midpoint uses averages instead: M = ((1 + 5)/2, (1 + 4)/2) = (3, 2.5). Differences measure change; averages locate the halfway point.
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First lesson in this subject: Complete the angle sum
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Practice · Use coordinates to compare distances, midpoints and moving points. Test relationships on a grid.
Book · Explore measurements, transformations, coordinates and geometric relationships through diagrams and worked examples.
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