Question
State whether the following statements are true or false. Justify your answer.
The points (0, 5), (0, -9) and (3, 6) are collinear.
The points (0, 5), (0, -9) and (3, 6) are collinear.
✓
Answer
False:Three points A, B, and C will be collinear if the area of $\triangle\text{ABC}=0$
$\Rightarrow\frac{1}{2}[\text{x}_1(\text{y}_2-\text{y}_3)+\text{x}_2(\text{y}_3-\text{y}_1)+\text{x}_3(\text{y}_1-\text{y}_2)]$
$\Rightarrow\frac{1}{2}[0(-9-6)+0(6-5)+3(5-(-9)]=0$
$\Rightarrow0+0+3(14)=0$
$\Rightarrow42\neq0,$ which is false.
Hence, the given points are not collinear.
$\Rightarrow\frac{1}{2}[\text{x}_1(\text{y}_2-\text{y}_3)+\text{x}_2(\text{y}_3-\text{y}_1)+\text{x}_3(\text{y}_1-\text{y}_2)]$
$\Rightarrow\frac{1}{2}[0(-9-6)+0(6-5)+3(5-(-9)]=0$
$\Rightarrow0+0+3(14)=0$
$\Rightarrow42\neq0,$ which is false.
Hence, the given points are not collinear.
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