let o be the origin a(3,-1) b(1,2) and c(1,1) the pair of points which are on different sides of the line 2x+3y=5 are?

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$$\begin{gathered} \mathrm{The} \mathrm{points} \mathrm{which} \mathrm{give} \mathrm{same} \mathrm{sign} \mathrm{when} \mathrm{we} \mathrm{put} \mathrm{them} \mathrm{in} \mathrm{line} \mathrm{are} \mathrm{on} \mathrm{same} \mathrm{side} \\ \mathrm{We} \mathrm{have} \\ \mathrm{L}: 2\mathrm{x}+3\mathrm{y}-5=0 \\ \mathrm{A}\left(3,-1\right), \mathrm{B}\left(1,2\right) \mathrm{and} \mathrm{C}\left(1,1\right) \\ \mathrm{L}\left(3,-1\right): 2\times 3+3\times \left(-1\right)-5=6-3=-2 \\ \mathrm{L}\left(1,2\right): 2\times 1+3\times 2-5=3 \\ \mathrm{L}\left(1,1\right): 2+3-5=0 \\ \mathrm{As} \mathrm{A}\left(3,-1\right) \mathrm{and} \mathrm{B}\left(1,2\right) \mathrm{are} \mathrm{having} \mathrm{different} \mathrm{sign}, \mathrm{hence} \mathrm{they} \mathrm{are} \mathrm{on} \\ \mathrm{other} \mathrm{side} \mathrm{of} \mathrm{line}. \end{gathered}$$

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