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# Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (- 1, - 1) are vertices of a right-angled triangle

**Solution:**

The vertices of the given triangles are A(4, 4), B (3, 5) and C (- 1, - 1).

It is known that the slope (m) of a non-vertical line passing through the points (x₁, y₁) and (x₂, y₂) is given by m = (y₂ - y₁)/(x₂ - x₁), x_{2} ≠ x₁

Therefore, slope of AB (m₁) = (5 - 4)/(3 - 4) = - 1

Slope of BC (m₂) = (- 1 - 5)/(- 1 - 3) = - 6/- 4 = 3/2

Slope of CA (m₃) = (4 + 1)/(4 + 1) = 5/5 = 1

It is observed that m₁m₃ = - 1

This shows that line segments AB and CA are perpendicular to each other i.e., the given triangle is right-angled at A(4, 4).

Thus, the points (4, 4), (3, 5) and (- 1, - 1) are the vertices of a right-angled triangle

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.1 Question 6

## Without using the Pythagoras theorem, show that the points (4, 4), (3, 5) and (- 1, - 1) are vertices of a right-angled triangle

**Summary:**

We proved that points A(4, 4), B (3, 5) and C (- 1, - 1) are vertices of the right-angled triangle without using the Pythagoras theorem

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