Question

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

Answer 1

Answer:

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

Answer 2

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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