Question
Show that the following points are collinear using determinants : P(5,1), Q(1, -1), R(11, 4)
$\begin{aligned} & Q\left(x_2, y_2\right)=Q(1,-1) \\ & R\left(x_2, y_2\right)=R(11,4)\end{aligned}$
If A(ΔPQR) = 0, then the points P, Q, R are collinear.
$\mathrm{A}(\Delta \mathrm{PQR})=\frac{1}{2}\left|\begin{array}{ccc}5 & 1 & 1 \\ 1 & -1 & 1 \\ 11 & 4 & 1\end{array}\right|$
$=\frac{1}{2}[5(-1-4)-1(1-11)$
$+1(4+11)]$
$\begin{aligned} & =\frac{1}{2}[5(-5)-1(-10)+1(15)] \\ & =\frac{1}{2}(-25+10+15)=0\end{aligned}$
∴ The points P, Q, R are collinear.Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
R = {(a, b) / b = |a – 1|, a ∈ Z, |a| < 3}