The value of m such that the points A(5, –2), B(8, –3) and C(m, –12) are collinear, is:

1. 29

2. 33

3. 35

4. 41

For three points A, B, and C to be collinear.

m_AB = m_BC

We know that,

m = $\dfrac{y$2 - y1}{x2 - x1}

Using A(5, -2) and B(8, -3) :

$m_{AB} = \dfrac{-3 - (-2)}{8 - 5} \\[1em] = \dfrac{-1}{3}.$

Using B(8, -3) and C(m, -12):

$m_{BC} = \dfrac{-12 - (-3)}{m - 8} \\[1em] = \dfrac{-9}{m - 8}$

m_AB = m_BC

⇒ $\dfrac{-1}{3} = \dfrac{-9}{m - 8}$

⇒ -1(m - 8) = -9 × 3

⇒ -m + 8 = -27

⇒ -m = -27 - 8

⇒ -m = -35

⇒ m = 35.

Hence, option 3 is the correct option.