Browse Questions

# State whether the following statement is true or false and justify : The points A (– 2, 1), B (0, 5), C (– 1, 2) are collinear

Toolbox:
• Area of a triangle is given by $\Delta = \large\frac{1}{2} | x_1 (y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$
• If the three points are collinear then $\Delta = 0$ (i.e) $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0$
Step 1 :
Let A(-2, 1) be $(x_1, y_1)$
$\quad \:$ B(0,5 ) be $(x_2, y_2)$
$\quad \:$ C(-1,2 ) be $(x_3, y_3)$
Substituting the above value in $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)$ we get,
$-2(5-3)+0(2-1)+(-1)(1-5)$
$= -4+0+4=0$
Hence the points are collinear.
Hence it is a true statement.