Mathematics for IGCSE & O level - Coordinate Geometry (Section 1 - No. 47)
If the line segment AB has coordinates A(1,3) and B(4,7), what is true?
The length of AB is 5.
The midpoint of AB is (2.5, 5).
The gradient of AB is 4/3.
The equation of AB is y = (4/3)x + 5/3.
Explanation
Length = √((4-1)^2 + (7-3)^2) = 5. Midpoint ((1+4)/2, (3+7)/2) = (2.5, 5). Gradient = (7-3)/(4-1) = 4/3. Equation: (y-3) = (4/3)(x-1) or y = (4/3)x + 5/3.
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