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Points A (3, 1), B (12, –2) and C (0, 2) cannot be the vertices of a triangle. Is the following statement true or false

Solution:

Given, the points are A(3, 1) B(12 , -2) and C(0, 2)

We have to determine if the given points represent the vertices of a triangle.

We know that,

A triangle can be formed from any three line segments provided the sum of the lengths of any two of the segments is greater than the length of the third.

The distance between two points P (x₁ , y₁) and Q (x₂ , y₂) is

√[(x₂ - x₁)²+(y₂ - y₁)²]

The length of AB = √[(12 - 3)²+(-2 - 1)²]

= √[(9)²+(-3)²]

= √(81 + 9)

= √90

AB = 3√10

The length of BC = √[(0 -12)²+(2 - (-2))²]

= √[(-12)²+(4)²]

= √(144 + 16)

= √160

BC = 4√10

The length of AC = √[(0 - 3)²+(2 - 1)²]

= √[(-3)²+(1)²]

= √(9 + 1)

AC = √10

Now, sum of the two sides of a triangle = AB + AC

= 3√10 + √10

= 4√10

= BC

So, AB + AC ⪈ BC

Therefore, the given points do not form the vertices of a triangle.

✦ Try This: Determine if the points D (2, 3), E (2, 5) and F (0, -4) cannot be the vertices of a triangle.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 5

Points A (3, 1), B (12, –2) and C (0, 2) cannot be the vertices of a triangle. Is the following statement true or false

Summary:

The statement “Points A (3, 1), B (12, –2) and C (0, 2) cannot be the vertices of a triangle” is true as it fails to satisfy the condition that the sum of the lengths of any two of the segments is greater than the length of the third

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