已知 $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right)$ 为直线 $y=-2 x+3$ 上的三个点, 且 $x_{1} < x_{2} < x_{3}$, 则以下判断正确的是 ( )
$\text{A.}$ 若 $x_{1} x_{2}>0$, 则 $y_{1} y_{3}>0$
$\text{B.}$ 若 $x_{1} x_{3} < 0$, 则 $y_{1} y_{2}>0$
$\text{C.}$ 若 $x_{2} x_{3}>0$, 则 $y_{1} y_{3}>0$
$\text{D.}$ 若 $x_{2} x_{3} < 0$, 则 $y_{1} y_{2}>0$