Coordinate Geometry-9

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Find the area of the triangle joining the points (1, -3), (3, 1), (1, 4)

Solution: Let (x1, y1) = (1, -3); (x2, y2) = (3, 1); (x3, y3) = (1, 4)

Area of Triangle = 1/2 [ x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2) ]

= 1/2 [1(1 - 4) + 3(4 + 3) + 1(-3 - 1)]

= 1/2 (-3 + 21 - 4) = 1/2 (14) = 7 square units.

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