Points m (-8: -3) n (-2: 6) k (4: -3) determine the kind of triangle which solution.

Analysis of the resulting triangle MNK shows that it is necessary to determine the lengths of the sides MN, NK and MK of this triangle.
To determine the lengths of the segments, we use the formula for calculating the distance between two points A (xa; ya) and B (xb; yb) on the Oxy plane: AB = √ [(xb – xa) ^ 2 + (yb – ya) ^ 2]. We have MN = √ [((- 2) – (–8)) ^ 2 + (6 – (–3)) ^ 2] = √ (36 + 81) = √ (117); NK = √ [(4 – (–2)) 2 + ((–3) – 6) ^ 2] = √ (36 + 81) = √ (117) and MK = √ [(4 – (–8)) ^ 2 + ((–3) – (–3) ^ 2] = √ (144 + 0) = √ (144) = 12.
The results obtained allow us to assert that MN = NK = √ (117). Therefore, the triangle MNK is an isosceles triangle.
Answer: Triangle MNK is an isosceles triangle.