Show that the points A


Show that the points A(-5, 1), B(5, 5) and C(10, 7) are collinear



Given: The points are A(-5, 1), B(5, 5) and C(10, 7).

Note: Three points are collinear if the sum of lengths of any sides is equal to the length of the third side.


$=2 \sqrt{29}$ units..........(1)

$B C=\sqrt{(10-5)^{2}+(7-5)^{2}}=\sqrt{25+4}$

$=\sqrt{29}$ units ...........(2)

$A C=\sqrt{(10+5)^{2}+(7-1)^{2}}=\sqrt{225+36}$

$=3 \sqrt{29}$ units .............(3)

From equations 1,2 and 3, we have

$A B+B C=A C$

Therefore, the three points are collinear.

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