Find the Area of the Triangle with Vertice at the Point: (−1, −8), (−2, −3) and (3, 2) - Mathematics

Question

Find the area of the triangle with vertice at the point:

(−1, −8), (−2, −3) and (3, 2)

Solution

$∆ = \frac{1}{2} | \begin{matrix} - 1 & - 8 & 1 \\ - 2 & - 3 & 1 \\ 3 & 2 & 1 \end{matrix} |$

$∆ = \frac{1}{2} | \begin{matrix} - 1 & - 8 & 1 \\ - 1 & 5 & 0 \\ 3 & 2 & 1 \end{matrix} | [Applying R_{2} \to R_{2} - R_{1}]$

$∆ = \frac{1}{2} | \begin{matrix} - 1 & - 8 & 1 \\ - 1 & 5 & 0 \\ 4 & 10 & 0 \end{matrix} | [Applying R_{3} \to R_{3} - R_{1}]$

$∆ = \frac{1}{2} | \begin{matrix} - 1 & 5 \\ 4 & 10 \end{matrix} |$

$∆ = \frac{1}{2} | - 10 - 20 |$

$∆ = \frac{1}{2} (30) = 15 square units$

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Applications of Determinants and Matrices

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Chapter 6: Determinants - Exercise 6.3 [Page 71]

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Chapter 6 Determinants
Exercise 6.3 | Q 1.3 | Page 71

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Find the Area of the Triangle with Vertice at the Point: (−1, −8), (−2, −3) and (3, 2) - Mathematics

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