Question

show that the following points from an equilateral triangle a(a,0),b(-a,0),c(0,a√3)​

Answer 1

Answer:

We have to show that abc is an equalateral

triangle

for answer please refer to the attachment

Step-by-step explanation:

hence three sides of triangle are equal it is an equaletral triangle

PLEASE MARK AS BRAINEST

Answer 2

Step-by-step explanation:

We Have :-

Vertices of Triangle ABC :-

A ( a , 0 )

B ( -a , 0 )

C ( 0 , a sqrt 3 )

To Show :-

These Points form an Equilateral Triangle

Formula Used :-

$distance \: formula \: = \sqrt{(a _{2} - a_{1}} )^{2} + \sqrt{ ({b_{2} - b_{1}} )^{2} }$

Solution :-

An Equilateral Triangle has all sides equal

so AB = BC = CA

AB :-

$\sqrt{(a + a} )^{2} + \sqrt{ ( 0 + 0 )^{2} } \\ \\ \\ \sqrt{ ( 2a)^{2} } \\ \\ \\ 2a$

BC :-

$\sqrt{ ( - a - 0 )^{2} } + \sqrt{ ( a \sqrt{3} - 0 )^{2} } \\ \\ \\ \sqrt{ ( a ^{2} + 3a^{2} ) } \\ \\ \\ \sqrt{ ( 4a^{2} )} \\ \\ \\ 2a$

CA :-

$\sqrt{ ( a - 0 )^{2} } + \sqrt{ ( a \sqrt{3} - 0 )^{2} } \\ \\ \\ \sqrt{ ( a ^{2} + 3a^{2} ) } \\ \\ \\ \sqrt{ ( 4a^{2} )} \\ \\ \\ 2a$

As AB = BC = CA

It is an equilateral triangle