Q12 of 23 Page 330

Let us calculate the area of triangular region formed by the three points (1, 4), (–1, 2) and (–4, 1)

Area of triangle is given by formula


Area = × [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]


Where (x1, y1), (x2, y2) and (x3, y3) are vertices of triangle


Here,


(x1, y1) is (1, 4)


⇒ x1 = 1 and y1 = 4


(x2, y2) is (-1, 2)


⇒ x2 = -1 and y2 = 2


(x3, y3) is (-4, 1)


⇒ x3 = -4 and y3 = 1


Hence substituting values in formula for area we get


Area = × [1(2 – 1) + (-1)(1 – 4) + (-4)(4 – 2)]


Area = × [1 + 3 + (-8)]


Area = × (-4)


Area = -2


Area cannot be negative


Area = 2 unit2


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