Name the type of triangle PQR formed by the points P (√2, √2), Q (-√2, -√2) and R (-√6, √6)

Solution:

Given, the points are P(√2, √2) Q(-√2, -√2) and R(-√6, √6)

We have to find the type of triangle PQR.

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

√[(x₂ - x₁)² + (y₂ - y₁)²]

Distance between P(√2, √2) and Q(-√2, -√2) = √[(-√2-√2)² + (-√2-√2)²]

= √[(-2√2)² + (-2√2)²]

= √(8 + 8)

= √16

= 4

Distance between Q(-√2, -√2) and R(-√6, √6) = √[(-√6+√2)²+(√6+√2)²]

By using algebraic identity,

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

So, QR = √[(√2)² + (√6)² - 2√2√6 + (√2)²+(√6)² + 2√2√6]

= √(2 + 6 + 2 + 6)

= √(8 + 8)

= √16

= 4

Distance between P(√2, √2) and R(-√6, √6) = √[(-√6 - √2)² + (√6 - √2)²]

√[(√2)² + (√6)² - 2√2√6 + (√2)² + (√6)² + 2√2√6]

= √(2 + 6 + 2 + 6)

= √(8 + 8)

= √16

= 4

PQ = QR = PR

An equilateral triangle is a triangle in which all three sides have the same length.

An equilateral triangle is also equiangular as all three internal angles are congruent to each other and are each 60°.

Therefore, PQR is an equilateral triangle.

✦ Try This: Name the type of triangle ABC formed by the points A (-2, 0), B (2, 0) and C (0, 2).

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

NCERT Exemplar Class 10 Maths Exercise 7.3 Sample Problem 3

Name the type of triangle PQR formed by the points P (√2, √2), Q (-√2, -√2) and R (-√6, √6)

Summary:

The type of triangle PQR formed by the points P (√2, √2), Q (-√2, -√2) and R (-√6, √6) is an equilateral triangle as all the three sides are of equal length

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