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Do the point (3,2),(-2,-3) and (2,3) from a triangle ? If so, name the type of triangle formed.​

Answer» <html><body><h2>Question</h2><p></p><h3>Do the point (3,<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>),(-2,-3) and (2,3) from a triangle ? If so, name the type of triangle formed.</h3><p></p><p></p><p></p><h2>GIVEN:</h2><p>Three <a href="https://interviewquestions.tuteehub.com/tag/points-1157347" style="font-weight:bold;" target="_blank" title="Click to know more about POINTS">POINTS</a></p><p></p><p>(3,2) , (-2,-3) , (2,3)</p><h2>TO FIND:</h2><p></p><p>Do these points form a triangle?, If yes then which type of triangle is formed?</p><p></p><h2>SOLUTION:</h2><p></p><p>There are two ways of finding while these points are forming triangle or not.</p><p></p><p>By <a href="https://interviewquestions.tuteehub.com/tag/plotting-20154" style="font-weight:bold;" target="_blank" title="Click to know more about PLOTTING">PLOTTING</a> the points in a graph</p><p>By calculating the area of figure formed by these points.</p><p>So, here we will do it by finding the area</p><p></p><h3>Using <a href="https://interviewquestions.tuteehub.com/tag/formula-464310" style="font-weight:bold;" target="_blank" title="Click to know more about FORMULA">FORMULA</a> to calculate area of triangle</h3><p></p><p>→ Area = 1/2 \mid∣ [ x_1x </p><p>1</p><p> </p><p> ( y_2y </p><p>2</p><p> </p><p> - y_3y </p><p>3</p><p> </p><p> ) + x_2x </p><p>2</p><p> </p><p> ( y_3y </p><p>3</p><p> </p><p> - y_1y </p><p>1</p><p> </p><p> ) + x_3x </p><p>3</p><p> </p><p> ( y_1y </p><p>1</p><p> </p><p> - y_2y </p><p>2</p><p> </p><p> ) ] \mid∣</p><p></p><p>→ Area = 1/2 | [ 3 ( -3 - (3) ) + (-2) ( 3 - 2 ) + 2 ( 2 - (-3) ) ] |</p><p></p><p>→ Area = 1/2 | [ -18 - 2 + 10 ] |</p><p></p><p>→ Area = 1/2 | [ -10 ] |</p><p></p><p>→ Area = 5 sq. units</p><p></p><p>Since, the area of figure formed by three points is not zero, it means three points are forming a triangle.</p><p></p><h2>Now,</h2><p></p><p>Let us take</p><p></p><p>A ( 3,2 ) , B ( -2,-3 ) , C ( 2,3 )</p><p>Then, Finding distances using distance formula</p><p></p><p>Distance = √[ ( x₁ - x₂ )² + ( y₁ - y₂ )² ]</p><p>→ AB = √[ (3 - (-2))² + ( 2 - (-3))² ]</p><p></p><p>→ AB = √( 25 + 25 ) = √50 units</p><p></p><p>→ BC = √[ (-2 - 2)² + (-3 - 3)² ]</p><p></p><p>→ BC = √( 16 + 36 ) = √52 units</p><p></p><p>→ AC = √[ (3 - 2)² + (2 - 3)² ]</p><p></p><p>→ AC = √( 1 + 1 ) = √2 units</p><p></p><p>Here, by Considering the lengths of sides of triangle</p><p></p><p>we can conclude that, lengths of AB, BC, and AC are forming a Pythagorean triplet;</p><p></p><p>BC² = AB² + AC²</p><p></p><p>( √52 )² = ( √50 )² + ( √2 )²</p><p></p><h3>It means these lines are forming a right angled triangle.</h3></body></html>


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