$P(x_1,y_1), Q(x_2,y_2), R(x_3,y_3)$ .

Denote three points as the following:
Using the diagram above, which of the following inequalities is/are TRUE? (
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Do NOT use a calculator. NO CHEATING!
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)

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(1.)
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$\quad \dfrac12<x_1<1$

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(2.)
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$\quad x_2<2x_1$

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(3.)
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$\quad x_2(x_1-1)>y_1(y_2-1)$

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(2.)$x_2y_2-x_3y_3=0$ .This was the original statement. Therefore R was denoted in the original context.