Question

with the help of a distance formula the point do not form a triangle A( 4, 2) B( 7, 5) ,C ( 9, 7)

Answer 1

Hey cool!! Here is answer for you.
distance formula AB = √(x2-x1)² + (y2 - y1)² right! and, come on we can use the formula now.
If you square AB, then AB² = x2-x1)² + (y2 - y1)² right!
A(4,2) B(7,5) C(9,7) right!
AB² = [7-4]²+[5-2]²
=9+9
=18
AB =√18 = 3√2.
BC² =[9-7]²+[7-5]²
=4+4
=8
BC=2√2.
AC² =[9-4]²+[7-2]²
=25+25
=50
AC=√50
=5√2.
Therefore, the three sides are founded right!
AB+BC=AC, because
3√2+2√2=5√2.
Therefore, the points are collinear, and so, they do not form a triangle.
Hope this will help you.

Answer 2

ab²=(7-4)²+(5-2)²
=9+9
ab=√18

bc²=(9-7)²+(7-5)²
=4+4=8
bc=√8

ac²=(9-4)²+(7-2)²
=25+25=50
ac=√50

in  a triangle , ab+bc>ac
√18+√8=7.071
√50=7.071

so it  is not possible