Question -
Answer -
Given:
x + y – 4 = 0, 3x – 7y– 8 = 0 and 4x – y – 31 = 0 forming a triangle and point (a, 2)is an interiorpoint of the triangle
Let ABC be thetriangle of sides AB, BC and CA whose equations are x + y − 4 = 0,3x − 7y − 8 = 0 and 4x − y − 31 = 0,respectively.
On solving them, weget A (7, – 3), B (18/5, 2/5) and C (209/25, 61/25) as thecoordinates of the vertices.
Let P (a, 2) be thegiven point.
It is given that pointP (a, 2) lies inside the triangle. So, we have the following:
(i) A and P must lieon the same side of BC.
(ii) B and P must lieon the same side of AC.
(iii) C and P must lieon the same side of AB.
Thus, if A and P lieon the same side of BC, then
21 + 21 – 8 – 3a – 14– 8 > 0
a > 22/3 … (1)
From (1), (2) and (3),we get:
A ∈ (22/3, 33/4)
∴ A ∈ (22/3, 33/4)