Q. 5 B5.0( 2 Votes )

# Show that the following points form an equilateral triangle.(a, 0), (−a, 0) and (0, a√3)

Formula used: (a, 0), (–a, 0) and (0, a√3)

Let the points be A (a, 0), B (–a, 0) and C (0, a√3)

Distance of AB

AB = √ ((–a – a)2 + (0 – 0)2)

AB = √ ((–2a)2 + (0)2)

AB = √ (4a2 + 0)

AB = √4a2

AB = 2a

Distance of BC

B C= √ ((0 – a)2 + (a√3 – 0)2)

BC = √ ((–a)2 + (a√3)2)

BC = √ (a2 + 3a2)

BC = √4a2

BC = 2a

Distance of AC

AC = √ ((0 – a)2 + (a√3 – 0))2)

AC = √ ((–a)2 + (a√3)2)

AC = √ (a2 + 3a2)

AC = √ 4a2

AC = 2a

AB = BC = AC = 2a

Since, all the sides are equal the points form an equilateral triangle.

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