Question

PLS HELP! I WILL MARK THE ANSWER AS BRAINLIEST..

Show that the points (a,a), (-a,-a) and (-√3a, √3a) are the vertices of an equilateral triangle.

Answer 1

Answer:

Here is the answer hope u will like it...

Step-by-step explanation:

Let A(a,a),B(−a,−a)andC(−

3a, 3

a) be the given points. Then, we have

AB= (−a−a) 2+(−a−a) 2= 4a 2 +4a

=2

2

a

BC=

(−

3

a+a)

2

+(

3

a+a)

2

BC=

a

2

(1−

3

)

2

+a

2

(

3

+1)

2

BC=a

(1−

3

)

2

+(1+

3

)

2

BC=a

1+3−2

3

+1+3+2

3

=a

8

=2

2

a

AC=

(−

3

a−a)

2

+(

3

a−a)

2

AC=

a

2

(

3

+1)

2

+a

2

(

3

−1)

2

AC=a

(

3

+1)

2

+(

3

)−1)

2

AC=a

3+1+2

3

+3+1−2

3

=a

8

=2

2

a

Clearly, we have

AB=BC=AC

Hence, the triangle ABC formed by the given points is an equilateral triangle.

Now,

Areaof△ABC=

4

3

(Side)

2

⇒Areaof△ABC=

4

3

×AB

2

⇒Areaof△ABC=

4

3

×(2

2a

)

2

sq.units=2

3

a

2

sq.units