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The Straight Lines — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines4 Marks
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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