The intersection of three lines x – y = 0, x + 2y = 3 and 2x + y = 6 is a

Correct Option - 2


Detailed Solution:

x – y = 0 . (i)

x + 2y = 3. (ii)

2x + y = 6 . (iii)

Solving (i) & (ii), we get (1, 1)

Solving (ii) & (iii), we get (3, 0)

Solving (iii) & (i), we get (2, 2)     

$AB=\sqrt[]{5,}BC=\sqrt[]{5},CA=\sqrt[]{2}$

$\therefore AB=BC$ Isosceles triangle

Hence, option (B) is correct answer.

<p>x – y = 0 . (i)</p><p>x + 2y = 3. (ii)</p><p>2x + y = 6 . (iii)</p><p>Solving (i) &amp; (ii), we get (1, 1)</p><p>Solving (ii) &amp; (iii), we get (3, 0)</p><p>Solving (iii) &amp; (i), we get (2, 2)&nbsp; &nbsp; &nbsp;</p><p>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1816682198"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;<math><mrow><mi>A</mi><mi>B</mi><mo>=</mo><mroot><mrow><mn>5</mn><mo>, </mo></mrow><mrow></mrow></mroot><mtext> </mtext><mtext> </mtext><mi>B</mi><mi>C</mi><mo>=</mo><mroot><mrow><mn>5</mn></mrow><mrow></mrow></mroot><mo>, </mo><mi>C</mi><mi>A</mi><mo>=</mo><mroot><mrow><mn>2</mn></mrow><mrow></mrow></mroot></mrow></math></p><p><math><mrow><mo>∴</mo><mi>A</mi><mi>B</mi><mo>=</mo><mi>B</mi><mi>C</mi></mrow></math>&nbsp;Isosceles triangle</p><p>Hence, option (B) is correct answer.</p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755156893phpdE9KWN.jpeg" alt="" width="229" height="205" loading="lazy"></picture></div></div>

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