Question

Question 3
The points (0,5), (0,-9) and (3,6) are collinear.

Answer 1

False
Here, $x_1=0,x_2=0,x_3=3,and{y}_1=5,y_2=-9,y_3=6\because \text{Area of triangle}\Delta =\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]\therefore \Delta =\frac{1}{2}\left[0\right(-9-6)+0(6-5)+3(5+9\left)\right]=\frac{1}{2}(0+0+3\times 14)=21\ne 0$
If the area of triangle formed by the points (0,5), (0-9) and (3,6) is zero, then the points are collinear.
Here, the area is not equal to zero, therefore, the points are non-collinear.