Question

6. Show that the following points form a equilateral
triangle A(a,0), B(-a,0), C(0, 3)​

Answer 1

Answer:

using distance formula

AB^2 = (a - -a)^2 + (0-0)^2

= (2a)^2

= 4a^2

BC^2 = (0- - a)^2 + (3-0)^2

= a^2 + 9

AC^2 = (a-0)^2 + (0-3)^2

= a^2 + 9

we can see that BC = AC, so the triangle is certainly an isosceles triangle. But, since value of a is not known, we cannot say with surity that the triangle is equilateral. For the triangle to be equilateral

a^2 + 9 = 4a^2

3a^2 = 9

a^2 = 3

a= +_√3

hence, the triangle would be equilateral only for a= +_√3, else it is an isosceles triangle.