Numerical answer
Find the area (in square units) of the triangle with vertices (2,3), (6,3) and (4,9).
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Answer: 12
Area = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| = ½|2(3−9) + 6(9−3) + 4(3−3)| = ½|−12+36+0| = ½×24 = 12. Shortcut: base = distance between (2,3) and (6,3) = 4 (horizontal), height = vertical distance from (4,9) to y=3 is 6, so area = ½×4×6 = 12.
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