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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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Gurleen Kaur

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