Answer :
Option B : [tex]\{51,149,140\}[/tex] will form a right angled triangle.
Option C : [tex]\{16,63,65\}[/tex] will form a right angled triangle.
Explanation:
Option A : [tex]\{1,1,1}\}[/tex]
To determine whether the coordinates will form a right angled triangle, let us apply the Pythagorean theorem.
Thus, we have,
[tex]1^2+1^2=1^2[/tex]
[tex]1+1=1[/tex]
[tex]2\neq 1[/tex]
Since, both sides are not equal.
The set [tex]\{1,1,1}\}[/tex] will not form a right angled triangle.
Hence, Option A is not the correct answer.
Option B : [tex]\{51,149,140\}[/tex]
Let us apply Pythagorean theorem.
Thus, we have,
[tex]51^2+140^2=149^2[/tex]
[tex]2601+19600=22201[/tex]
[tex]22201=22201[/tex]
Since, both sides are equal.
The set [tex]\{51,149,140\}[/tex] will form a right angled triangle.
Hence, Option B is the correct answer.
Option C : [tex]\{16,63,65\}[/tex]
Let us apply Pythagorean theorem.
Thus, we have,
[tex]16^2+63^2=65^2[/tex]
[tex]256+3969=4225[/tex]
[tex]4225=4225[/tex]
Since, both sides are equal.
The set [tex]\{16,63,65\}[/tex] will form a right angled triangle.
Hence, Option C is the correct answer.
Option D : [tex]\{6,11,8\}[/tex]
Let us apply Pythagorean theorem.
Thus, we have,
[tex]6^2+8^2=11^2[/tex]
[tex]36+64=121[/tex]
[tex]100\neq 121[/tex]
Since, both sides are not equal.
The set [tex]\{6,11,8\}[/tex] will not form a right angled triangle.
Hence, Option D is not the correct answer.