Question

Show that the point P(1,1) lies on thr line segment joining the points A(3,-2) and B(-1,4)

Answer 1

P(1,1)
A(3,-2)
B(-1,4)

If point P is on line segment AB then

PA=√4+9 =√13
AB=√16+36=√52
BP= √4+9

Answer 2

Answer:

$(1,1) \:point \\lie \:on \: joining \:the\\points\: A\:and \:B$

Step-by-step explanation:

$Let \:given \: points \\P(1,1),\:A(3,-2)\:and \:B(-1,4)$

$Then\:x_{1}=1,y_{1}=1; \:\:x_{2}=3,y_{2}=-2; \\\:x_{3}=-1,y_{3}=4;$

$We\:know,\\Area\:of\:\triangle\\=\frac{1}{2}|x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})|\\Area \:of\:\triangle PAB\\=\frac{1}{2}|1(-2-4)+3(4-1)+(-1)(1+2)|\\=\frac{1}{2}|1\times (-6)+3\times 3+(-1)\times 3|\\=\frac{1}{2}|-6+9-3|\\=\frac{1}{2}\times 0\\=0$

$P,\:A\: and\: B\: are\: collinear.$

Therefore,

$(1,1) \:point \\lie \:on \: joining \:the\\points\: A\:and \:B$

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