Question

If A(2,7), B(8,3) and C(14, -1) are collinear then which of the following is
true.
1) AB + BC = AC
2) AC + CB = AB
3) AB + AC = BC
4) All the above​

Answer 1

The option (1) is the correct choice .

Given that the points A(2,7), B(8,3) and C(14, -1) are collinear .

Using the distance formula to find the distance between two points -

D = √((x1 - x2)² + (y1 - y2)²)

Distance between the points A(2,7) and B(8,3)

AB = √((2-8)² + (7-3)²)

AB = √52

Distance between the points A(2,7) and C(14,-1)

AC = √((2-14)² + (7+1)²)

AC = √208

Distance between the points B(8,3) and C(14,-1)

BC = √((8-14)² + (3+1)²)

BC = √52

Proving that , AB + BC = AC

=> AB + BC = AC

=> √52+√52 = √208

=> 2√52 = √208

=> √208 = √208

Hence , proved

Therefore , the option (1) is the correct choice.

Answer 2

Answer:

 all the above

Step-by-step explanation:

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