Question

If the points A(2, 3), B(5, k) and C(6, 7) are collinear then ______.

Options

• k = 4

• k = 6

• `k = (-3)/2`

• `k = 11/4`

Answer 1

If the points A(2, 3), B(5, k) and C(6, 7) are collinear then k = 6.

Explanation:

For collinearity slopes AB and AC must be equal.

Slope `AB = (k - 3)/(5 - 2)`

= `(k - 3)/3`

Slope `AC = (7 - 3)/(6 - 2)`

= `4/4`

= 1

Set `(k - 3)/3 = 1`

⇒ k – 3 = 3

⇒ k = 6