Example 17 - Find area of triangle (3, 8), (-4, 2), (5, 1) - Examples

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  1. Chapter 4 Class 12 Determinants
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Example 17 Find the area of the triangle whose vertices are (3, 8), (– 4, 2) and (5, 1). The area of triangle is given by ∆ = 1﷮2﷯ x1﷮y1﷮1﷮x2﷮y2﷮1﷮x3﷮y3﷮1﷯﷯ Here x1 = 3 , y1 = 8, x2 = – 4 , y2 = 2, x3 = 5 , y3 = 1 ∆ = 1﷮2﷯ 3﷮8﷮1﷮−4﷮2﷮1﷮5﷮1﷮1﷯﷯ = 1﷮2﷯ 3 2﷮1﷮1﷮1﷯﷯−8 −4﷮1﷮5﷮1﷯﷯+1 −4﷮2﷮5﷮1﷯﷯﷯ = 1﷮2﷯ (3( 2 – 1) – 8 ( – 4 – 5) + 1 ( – 4 – 10) ) = 1﷮2﷯ (3 (1) – 8 ( – 9) + 1 ( – 14)) = 1﷮2﷯ (3 + 72 – 14) = 61﷮2﷯ Thus, the required area of triangle is 𝟔𝟏﷮𝟐﷯ square units

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