Answer:
[tex]L_{ab}=\sqrt{73}\\L_{ac}=2\\L_{bc}=\sqrt{65}[/tex]
It's a scalene triangle
Step-by-step explanation:
Distance between two points
The distance L between the points P(a,b), Q(c,d) is computed by
[tex]\displaystyle L=\sqrt{(d-b)^2+(c-a)^2}[/tex]
We are given 3 points A(7,3), B(-1,0), C(7,1)
Let's find all three distances
[tex]\displaystyle L_{ab}=\sqrt{(0-3)^2+(-1-7)^2}=\sqrt{9+64}=\sqrt{73}[/tex]
[tex]\displaystyle L_{ac}=\sqrt{(1-3)^2+(7-7)^2}=\sqrt{4+0}=2[/tex]
[tex]\displaystyle L_{bc}=\sqrt{\left (1-0\right )^2+(7+1)^2}=\sqrt{1+64}=\sqrt{65}[/tex]
Since the three sides are different it's a scalene triangle
