Question

Determine if the points (1,5),(2,3), and (-2, -11) are collinear.​

Answer 1

Answer: Here is ur answer

Step-by-step explanation:

Answer 2

$\huge\underline\mathrm{SOLUTION:-}$

Let,

• A = (1,5)
• B = (2,3)
• C = (-2, -11)

Using Distance Formula to find distance AB, BC, and CA.

___________________________

$AB = \sqrt{(2 - 1) {}^{2} + (3 - 5) {}^{2} }$

$= \sqrt{(1) {}^{2} + ( - 2) {}^{2} }$

$= \sqrt{1 + 4}$

$= \sqrt{5}$

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$BC \: = \sqrt{( - 2 - 2) {}^{2} + ( - 11 - 3) {}^{2} }$

$= \sqrt{( - 4) {}^{2} + ( - 14) {}^{2} }$

$= \sqrt{16 + 196 }$

$= \sqrt{212}$

$= 2 \sqrt{53}$

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$CA = \sqrt{( - 2 - 1) {}^{2} + ( - 11 - 5) {}^{2} }$

$= \sqrt{( - 3) {}^{2} + ( - 16) {}^{2} }$

$= \sqrt{9 + 256}$

$= \sqrt{265}$

___________________________

Since, AB + AC ≠ BC,

BC + AC ≠ AB and AC ≠ BC.

ThereFore:

• The points A, B and C are not collinear.

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