Determine the nature of triangle formed by A(0,0), B(4,0), C(4,3).
Right-angled scalene triangle
Using the distance formula, find the length of each side of triangle ABC.
\(AB = \sqrt{(4-0)^2+(0-0)^2} = \sqrt{16} = 4\).
\(BC = \sqrt{(4-4)^2+(3-0)^2} = \sqrt{9} = 3\).
\(AC = \sqrt{(4-0)^2+(3-0)^2} = \sqrt{16+9} = \sqrt{25} = 5\).
Since \(AB^2+BC^2 = 16+9 = 25 = AC^2\), the triangle satisfies the Pythagorean theorem, so it is right-angled at B.
All three sides (4, 3, 5) are of different lengths, so the triangle is scalene as well. Hence it is a right-angled scalene triangle.
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