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Midpoint of a Line Segment Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Midpoint formula
The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂)/2, (y₁ + y₂)/2).
Purpose of midpoint formula
The midpoint formula is used to find the exact middle point of a line segment between two given points.
Midpoint of (2, 4) and (6, 8)
The midpoint is ((2 + 6)/2, (4 + 8)/2) = (4, 6).
Midpoint of (−3, 5) and (7, −1)
The midpoint is ((−3 + 7)/2, (5 + (−1))/2) = (2, 2).
Midpoint of a horizontal line
If the line is horizontal, the y-coordinates of the endpoints are the same, so the midpoint is the average of the x-coordinates.
Midpoint of a vertical line
If the line is vertical, the x-coordinates of the endpoints are the same, so the midpoint is the average of the y-coordinates.
Midpoint of (0, 0) and (10, 0)
The midpoint is ((0 + 10)/2, (0 + 0)/2) = (5, 0).
Midpoint of (−4, −6) and (4, 6)
The midpoint is ((−4 + 4)/2, (−6 + 6)/2) = (0, 0).
Midpoint in coordinate geometry
The midpoint is a key concept in coordinate geometry, often used to divide a line segment into two equal parts.
Finding one endpoint given midpoint and other endpoint
If the midpoint is (xm, ym) and one endpoint is (x₁, y₁), the other endpoint is (2xm − x₁, 2ym − y₁).
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