Question

If (5, 7), (3,P) and (6,6) are collinear, then the value of P is

Answer 1

Hope this will help you.

Answer 2

The value of P is 9.

Given data:

The points (5, 7), (3, P) and (6, 6) are collinear

To find:

The value of P

Concept:

We can find the area of three collinear points being 0.

OR, one point lies on the straight line formed by other two points.

Step-by-step explanation:

The area of the triangle formed by the points (5, 7), (3, P) and (6, 6) is

½ |5 (P - 6) + 3 (6 - 7) + 6 (7 - P)| unit²

= ½ |5P - 30 - 3 + 42 - 6P| unit²

= ½ |- P + 9| unit²

Since the given three points are collinear,

½ |- P + 9| = 0

⇒ P = 9

Thus the value of P is 9.

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