Show that the points A

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.

$\mathrm{AB}=\sqrt{(5+5)^{2}+(5-1)^{2}}=\sqrt{100+16}$

$=2 \sqrt{29}$ 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.