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  • Need solution for RD Sharma maths class 12 chapter Determinants exercise 5.3 question 12 subquestion (i)

Need solution for RD Sharma maths class 12 chapter Determinants exercise 5.3 question 12 subquestion (i)

Answers (1)

\boldsymbol{Answer\! :} 2x=y

\boldsymbol{Hints\! :} Take\; the\; third\; point\; as\; (x,y)\; and\;\; use\; the\; f\! ormula\; o\! f\; area\; o\! f\; triangle\; and\; equate\; it\; with\; zero.

Given: (1,2) and (3,6)

Explanation: Vertices are (1,2) and (3,6)
                        Let\; the\; third\; point\; be\; (x,y)

Determinant= \Delta =0

\Delta =\frac{1}{2}\begin{vmatrix} X_{1} &Y_{1} &1 \\ X_{2} &Y_{2} &1 \\ X_{3} &Y_{3} &1 \end{vmatrix}=0

    \Rightarrow \frac{1}{2}\begin{vmatrix} x &y &1 \\ 1 &2 &1 \\ 3 &6 &1 \end{vmatrix}=0

    \Rightarrow x\left|\begin{array}{ll} 2 & 1 \\ 6 & 1 \end{array}\right|-y\left|\begin{array}{cc} 1 & 1 \\ 3 & 1 \end{array}\right|+1\left|\begin{array}{cc} 1 & 2 \\ 3 & 6 \end{array}\right|=0

    \Rightarrow x(2-6)-y(1-3)+1(6-6)=0

    \Rightarrow -4x+2y+0=0

    \Rightarrow -4x+2y=0

    \Rightarrow -2x+y=0

    \Rightarrow 2x=y

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