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Home » 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. Solution:
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. Solution:
CBSE | Class 11 | Exercise 23.14 | Maths | RD Sharma | Straight Lines
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. Solution:

According to ques,:

    \[x\text{ }+\text{ }y\text{ }\text{ }4\text{ }=\text{ }0,\]

    \[3x\text{ }\text{ }7y\text{ }+\text{ }8\text{ }=\text{ }0,\]

And

    \[4x\text{ }\text{ }y\text{ }\text{ }31\text{ }=\text{ }0\]

forming a triangle and point (-3, 2)

Let ABC be the triangle of sides AB, BC and CA, whose equations:

    \[~x\text{ }+\text{ }y~-~4\text{ }=\text{ }0,\]

    \[3x~-~7y\text{ }+\text{ }8\text{ }=\text{ }0\]

and

    \[4x~-~y~-~31\text{ }=\text{ }0,\]

respectively.

On solving them, we get A (7, – 3), B (2, 2) and C (9, 5) as the coordinates of the vertices.

Let P (− 3, 2) be the given point.

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 73

The given point P (− 3, 2) will lie inside the triangle ABC, if

(i) A and P lies on the same side of BC

(ii) B and P lies on the same side of AC

(iii) C and P lies on the same side of ABThus, if A and P lie on the same side of BC, then

    \[21\text{ }+\text{ }21\text{ }+\text{ }8\text{ }\text{ }9\text{ }\text{ }14\text{ }+\text{ }8\text{ }>\text{ }0\]

    \[50\text{ }\times \text{ }\text{ }15\text{ }>\text{ }0\]

Or ,

    \[-750\text{ }>\text{ }0\]

,

This is false

∴ The point (−3, 2) lies outside triangle ABC.

 

i

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