Question

5. Show that the points A(a,0), B(-a,0), C(0, a√13 ) form an equilateral triangle.​

Answer 1

Answer:

Given  A(a,0) B(−a,0) C(0,a3)

AB=(a−(−a))2+(0−0)2=4a2=2a

BC=(0−(−a))2+(a3)2=4a2=2a

CA=(0−(−a))2+(a3)2=4a2=2a

∴ AB= BC = CA

 Hence it is an equilateral triangle

Step-by-step explanation:

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Answer 2

Answer:

GivenA(a,0),B(-a,0),C(0,a√3)

AB=√( a - (- a) ) square+( 0 - 0 ) square=√4a square = 2a

BC=

(0−(−a))

2

+(a

3

)

2

=

4a

2

=2a

CA=

(0−(−a))

2

+(a

3

)

2

=

4a

2

=2a

∴ AB= BC = CA