Show that the points (2,-2),(-3,8)&(-1,4) are …
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Sia ? 6 years, 2 months ago
Using distance formula
AB = {tex}\sqrt { ( - 3 - 2 ) ^ { 2 } + [ 8 - ( - 2 ) ] ^ { 2 } }{/tex}
{tex}= \sqrt {(- 5) ^ { 2 } + 10 ^ { 2 } } = \sqrt { 25 + 100 }{/tex}
{tex}= \sqrt { 125 } {/tex} {tex}= 5 \sqrt { 5 }{/tex} units
BC = {tex}\sqrt { [ - 1 - ( - 3 ) ] ^ { 2 } + ( 4 - 8 ) ^ { 2 } }{/tex}
{tex}= \sqrt { 2 ^ { 2 } + (-4) ^ { 2 } } = \sqrt { 4 + 16 } = \sqrt { 20 }{/tex}
{tex}= 2 \sqrt { 5 }{/tex} units
AC = {tex}\sqrt { ( - 1 - 2 ) ^ { 2 } + [ 4 - ( - 2 ) ] ^ { 2 } }{/tex}
{tex}= \sqrt { (-3) ^ { 2 } + 6 ^ { 2 } } = \sqrt { 9 + 36 } = \sqrt { 45 }{/tex}
{tex}= 3 \sqrt { 5 }{/tex} units
{tex}\because 2 \sqrt { 5 } + 3 \sqrt { 5 } = 5 \sqrt { 5 }{/tex}
{tex}\therefore{/tex} Points are collinear.
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