Math, asked by chinmay53001, 9 months ago

Prove that (1,4),(_1,2) and (_5,_2) points are collinear by using distance formula find out

Answers

Answered by nirushreju1
0

Answer:

AB + BCis equal to AC so the points are collinear...

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Answered by decentdileep
0

Given A(1,4) B(-1,2) C(-5,-2)

Distance formula=

 \sqrt({x2 - x1})^{2}  + (y2 -  {y1})^{2}  \\ ab = (\sqrt{ - 1 - 1 )^{2} }  + (2 - 4 ) ^{2}  \\   = \sqrt{( - 2})^{2}  +  {( - 2})^{2}  \\   = \sqrt{4 + 4}  \\   = \sqrt{8}  \\  = 2  \ \sqrt{2}  \\ bc =  \sqrt{ - 5 - ( - 1) ^{2} }  +  ({ - 2 - 2)}^{2} \\  =  \ \sqrt{( - 5 + 1} )^{2}  + ( { - 2 - 2})^{2} \\  =  \sqrt{ (- 4} )^{2}  +  ({ - 4})^{2}  \\   =  \sqrt{16 + 16}   \\ =  \sqrt{32}  \\  = 2 \sqrt{2}  \\ ac =  \sqrt{ (- 5 - 1} )^{2}  + ( - 2 - 4 )^{2}  \\   = \sqrt{ (- 6})^{2} +  ({ - 6})^{2}  \\  \sqrt{36 + 36}  \\  =  \sqrt{72} \\  = 6\sqrt{2}

AB, BC&AC are collinear

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