Name the type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5)

Solution:

Given, the points are A(-5, 6) B(-4, -2) and C(7, 5)

We have to find the type of triangle ABC.

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

√[(x₂ - x₁)² + (y₂ - y₁)²]

Distance between A(-5, 6) and B(-4, -2) = √[(-4 - (-5))² + (-2 - 6)²]

= √[(1)² + (-8)²]

= √(1 + 64)

= √65

Distance between B(-4, -2) and C(7, 5) = √[(7 - (-4))² + (5 - (-2))²]

= √[(11)² + (7)²]

= √(121 + 49)

= √170

Distance between A(-5, 6) and C(7, 5) = √[(7 - (-5))² + (5 - 6)²]

= √[(12)² + (-1)²]

= √(144 + 1)

= √145

We know that a scalene triangle is a triangle in which all three sides have different lengths.

AB ≠ BC ≠ AC

The three sides of the triangle are in different lengths.

Therefore, the given points represent a scalene triangle.

✦ Try This: Name the type of the triangle formed by the vertices (1, 1) (3, 2) and (2, 4).

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

NCERT Exemplar Class 10 Maths Exercise 7.3 Problem 1

Name the type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5)

Summary:

The type of triangle formed by the points A (–5, 6), B (–4, –2) and C (7, 5) is a scalene triangle as the sides of the triangle have different lengths

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