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What will be the area of a triangle whose vertices are (3, 1), (0, 4) and (5, 9)?(a) 5 units(b) -5 units(c) -15 units(d) 15 unitsI had been asked this question in an interview for internship.The query is from Geometry in section Coordinate Geometry of Mathematics – Class 10

Answer»

Correct choice is (c) -15 UNITS

To explain I would say: We know that, area of triangle = \(\FRAC {1}{2}\){x1(y2 – Y3) + x2(y3 – y1) + X3(y1 – y2 )}

The coordinates of vertices of the triangle are (3, 1), (0, 4) and (5, 9).

The area of triangle = \(\frac {1}{2}\){3(4 – 9) + 0(9 – 1) + 5(1 – 4) } = \(\frac {1}{2}\) {-15 + 0 – 15} = \(\frac {-30}{2}\) = -15 units

Since area of triangle cannot be zero. So area of triangle is 15 units.



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