Question

The points $(0,5),(0,-9)$ and $(3,6)$ are collinear. State whether the following statement is true or false. Justify your answer.

• A. True
• B. False

Answer 1

The correct option is B False

Explanation.

The points are collinear if area of a triangle formed by its points is equals to the zero.

$$\begin{gathered} x_1=0,x_2=0,x_3=3 \\ {y}_1=5,y_2=–9,y_3=6 \end{gathered}$$

The area of triangle is given by

$$\begin{gathered} A=\frac{1}{2}\left[x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right] \\ =\frac{1}{2}\left[0\left(-9-6\right)+0\left(6-5\right)+3\left(5+9\right)\right] \\ =\frac{1}{2}\left[42\right] \\ =21\ne 0\begin{array}{}\\ \\ \end{array} \end{gathered}$$

Hence, the given statement is False.