n4tbcNelizar
n4tbcNelizar n4tbcNelizar
  • 17-07-2016
  • Mathematics
contestada

the coordinates p(0, 1), q(3, 2), r(5, -4) form a right triangle.true or false

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dalendrk
dalendrk dalendrk
  • 17-07-2016
[tex]P(0;\ 1);\ Q(3;\ 2);\ R(5;-4)\\\\\vec{PQ}=[3-0;\ 2-1]=[3;\ 1]\\\vec{PR}=[5-0;-4-1]=[5;-5]\\\vec{QR}=[5-3;-4-2]=[2;-6]\\\\\vec{a}\perp\vec{b}\iff\vec{a}\circ\vec{b}=0\\\vec{a}=[x_1;\ y_1];\ \vec{b}=[x_2;\ y_2]\to \vec{a}\circ\vec{b}=x_1x_2+y_1y_2\\\\\vec{PQ}\circ\vec{QR}=[3;\ 1]\circ[2;-6]=3\cdot2+1\cdot(-6)=6-6=0\\\\Answer:\boxed{TRUE;\ |\angle PQR|=90^o}[/tex]
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