Question

A triangle has verticies of (1,3) (4,5) and (6,2). Is this a right angle triangle? Solve using algebra.

Answer 1

find the distances between the points (all three, two at a time)

if the distances satisfy .... a^2 + b^2 = c^2
... then it is a right triangle

Answer 2

or:
if right angled, then two lines must be perpendicular

slope between 1st point and 2nd = 2/3
slope between 1st and third = -1/5
slope between 2nd and 3rd = -3/2

notice that 2/3 and -3/2 are negative reciprocals of each other, thus , yes we have a right-angled triangle