Show that the points (a,a), (-a,-a) …
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Preeti Dabral 1 year, 11 months ago
Let A(a, a), B(-a, -a) C{tex}\left( { - \sqrt 3 a,,\sqrt 3 a} \right){/tex}
{tex}AB = \sqrt {{{( - a - a)}^2} + {{( - a - a)}^2}} = \sqrt {8{a^2}} = 2\sqrt 2 a{/tex}
{tex}BC = \sqrt {{{( - \sqrt 3 a + a)}^2} + {{(\sqrt 3 a + a)}^2}} = 2\sqrt 2 a{/tex}
{tex}AC = \sqrt {{{( - \sqrt 3 a - a)}^2} + {{(\sqrt 3 a - a)}^2}} = 2\sqrt 2 a{/tex}
{tex}\therefore {/tex} AB = BC = AC = {tex}2\sqrt 2 a{/tex}
{tex}ar\Delta ABC = \frac{{\sqrt 3 }}{4} \times {(side)^2}{/tex}
{tex} = \frac{{\sqrt 3 }}{4} \times \left( {2\sqrt 2 a} \right)^2{/tex}
{tex} = 2\sqrt 3 {a^2}{/tex} sq. units
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