Q. 5 B5.0( 2 Votes )

# Show that the following points form an equilateral triangle.

(a, 0), (−a, 0) and (0, a√3)

Answer :

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 = √ (4a^{2} + 0)

⇒ AB = √4a^{2}

⇒ AB = 2a

Distance of BC

⇒ B C= √ ((0 – a)^{2} + (a√3 – 0)^{2})

⇒ BC = √ ((–a)^{2} + (a√3)^{2})

⇒ BC = √ (a^{2} + 3a^{2})

⇒ BC = √4a^{2}

⇒ BC = 2a

Distance of AC

⇒ AC = √ ((0 – a)^{2} + (a√3 – 0))^{2})

⇒ AC = √ ((–a)^{2} + (a√3)^{2})

⇒ AC = √ (a^{2} + 3a^{2})

⇒ AC = √ 4a^{2}

⇒ AC = 2a

∴ AB = BC = AC = 2a

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

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