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  • Need solution for RD Sharma maths class 12 chapter Determinants exercise 5.3 question 8

Need solution for RD Sharma maths class 12 chapter Determinants exercise 5.3 question 8

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Answer: 46 sq. units

Hints: To find area of triangle use modulus in the formula of determinant.

Given: (-3,5), (3, -6) and (7,2).

Explanation: Vertices are (-3,5), (3, -6) and (7,2).

\text { Area of triangle is } \Rightarrow|\Delta|=\left | \frac{1}{2}\begin{vmatrix} -3 &5 &1 \\ 3 &-6 &1 \\ 7 &2 &1 \end{vmatrix} \right |

                                                    =\left | \frac{1}{2}\left(-3\left|\begin{array}{cc} -6 & 1 \\ 2 & 1 \end{array}\right|-5\left|\begin{array}{cc} 3 & 1 \\ 7 & 1 \end{array}\right|+1\left|\begin{array}{cc} 3 & -6 \\ 7 & 2 \end{array}\right|\right) \right |

                                                   =\left | \frac{1}{2}[-3(-6-2)-5(3-7)+1(6-(-42))] \right |

                                                   =\left | \frac{1}{2}[-3(-8)-5(-4)+1(48)] \right |

                                                   \Rightarrow \frac{1}{2}\left | 92 \right |

                                                   \Rightarrow 46sq. units

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