Question

Show that the following points taken in order form an equilateral triangle in each case.
(i) A(2, 2), B(–2, –2), C^-2 3,2 3h (ii) A^ 3,2h , B (0,1), C(0,3)

Answer 1

what you know about equilateral triangle? sides of it are equal , of course it is .
so, first of all we have to find out sides of equilateral triangle. now, Let's do it.

(i) A(2,2) , B(-2,-2) and C= (-2√3,2√3)
use distance formula,
length of AB = √{(-2-2)² + (-2-2)²} = 4√2 unit
length of BC = √{(-2+2√3²+(-2-2√3)²}
= √{2(2² + 2²√3²)} unit
= √{2(4 + 12)} = 4√2 unit
length of CA = √{(2+2√3)²+(2-2√3)²}
= √2(4 + 12) = 4√2 unit
here, AB = BC = CA
then, ABC is an equilateral triangle.

(ii) A = (√3,2) , B = (0,1) and C = (0,3)
length of AB = √{√3² + (2 - 1)² = 2 unit
length of BC = √{(0-0)² + (3 - 1)² = 2 unit
length of CA = √{(0 - √3)² + (3 - 2)²} = 2 unit
here, AB = BC = CA
so, ABC is also an equilateral triangle

Answer 2

Step-by-step explanation:

answer are here refere it