Analytic geometry

Question

Given TRIANGLE with vertices A(-5,2) B(-1,6) C(5,0)

a) determine the lengths and the slopes of each of the sides of triangle ABC

n) what TYPE of triangle is ABC? Justify your answer

Answer 1

sides are 4sqr2, 6sqr2 and 2sqr29

the sum of squares of the two smaller sides is less than the square of the longest side

108 < 116

so, it's an obtuse triangle, 2 acute angles, one obtuse angle opposite the longest side

had the longest side been 108, it would have been a right triangle.

had the longest side been less than 108, it would have been a triangle with 3 acute angles.