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| 1. |
Check whether (5,-2) (6,4) & (7,-2) are the vertices of an isoceles triangle |
| Answer» Let A {tex}\\rightarrow{/tex} (5, -2), B {tex}\\rightarrow{/tex} (6, 4) and C {tex}\\rightarrow{/tex} (7, -2)Then,{tex}AB = \\sqrt {{{(6 - 5)}^2} + {{(4 - ( - 2))}^2}} = \\sqrt {{{(1)}^2} + {{(6)}^2}}{/tex}{tex} = \\sqrt {1 + 36} = \\sqrt {37}{/tex}{tex}BC = \\sqrt {{{(7 - 6)}^2} + {{( - 2 - 4)}^2}} = \\sqrt {{{(1)}^2} + {{( - 6)}^2}}{/tex}{tex}= \\sqrt {1 + 36} = \\sqrt {37}{/tex}We see that AB = BCtherefore, ABC is an isosceles triangle.Let D be the mid-point of BC. Then, coordinates of D are {tex}\\left( \\frac { 5 + 7 } { 2 } , \\frac { - 2 - 2 } { 2 } \\right){/tex}\xa0i.e, (6, -2)Therefore, AD =\xa0{tex}\\sqrt { ( 6 - 6 ) ^ { 2 } + ( 4 + 2 ) ^ { 2 } } = \\sqrt { 36 } = 6{/tex} | |