Determine whether the point (-3, 2) lies inside or outside the tr… - Vidyadip

Question

Determine whether the point (-3, 2) lies inside or outside the triangle whose sides are given by the equations x + y - 4 = 0, 3x - 7y + 8 = 0, 4x - y - 31 = 0.

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Answer

Let ABC be the triangle, then coordinates of the vertices are marked in the following figure.
p(-3, 2) lie inside if.
A and P, B and P, C and P lie on the same side of BC, AC and BA respectively.
If A and P lie on the same jside of bc then,
(3(7) - 7(-3) + 8)(3(-3) - 7(2) + 8) > 0
(21 + 21 + 8)(-9 - 14 + 8) > 0
But, (50)(-15) is not > 0
$\therefore$ The point (-3, 2) is outside ABC.

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