Question

Show that (2, 1), (1, 1), (3, 3) are
the vertices of an equilateral
traingle.​

Answer 1

Answer:

we know, any triangle is said to be equilateral triangle when all sides of triangle be equal.

so, use distance formula and find length of all sides of given triangle.

if (x1, y1) and (x2, y2) two points are given then, distance between them = √{(x1 - x2)² +(y1 - y2)²}

Let A = (-1, -1) , B = (1, 1) and C = (-√3, √3)

length of side AB = √{(-1 - 1)² + (-1 - 1)²}

= √{(-2)² + (-2)²}

= √{4 + 4} = √8

=2√2

length of side BC = √{(-1 + √3)² + (-1 - √3)²}

= √{√3² + 1² - 2√3 + √3² + 1² + 2√3}

= √{3 + 1 + 3 + 1}

= √{8}

= 2√2

length of side CA = √{(-√3 + 1)² + (√3 + 1)²}

= √{√3² + 1² - 2√3 + √3² + 1² + 2√3}

= √{3 + 1 + 3 + 1 }

= √8

= 2√2

here we see that length of side AB = length of side BC = length of side CA

so, ABC is an equilateral triangle.

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