Find the length of each side of the triangle determined by t

Find the length of each side of the triangle determined by the three points P1, P2, and P3. State whether the
triangle is an isosceles triangle, a right triangle, neither of these, or both.
P₁ = (-5, -4), P₂ = (-3, 4), P₃ = (0, -1)

a.   d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 34
both
b.   d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 5 2
neither
c.   d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 34
isosceles triangle
d.   d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 5 2
right triangle

Solution

p1=(-5,-4) , p2=(-3,4) , p3=(0,-1)

d(p1,p2)= sqrt ((4+4)²+(-3+5)²)= 2 sqrt17

d(p2,p3)= sqrt((-1-4)²+(0+3)²)=sqrt 34

d(p1,p3)=sqrt ((-1+4)²+(0+5)²)= sqrt 34

Here the length of two sides are same.Therefore the triangle is isosceles

sqrt34²+ sqrt34²=c²

34 +34=c²

c=2sqrt17 which is the length of third side

Hence its a right angle triangle

Therefore the correct option is a