Determine the type of triangle defined by the coordinates of its vertices: M (–8; – 3), N (–2; 6), K (4; –3).

First, we calculate the lengths of the sides MN, NK and MK of the triangle MNK with vertices M (–8; –3), N (–2; 6), K (4; –3). To do this, use the formula for calculating the distance between two points A (xa; ya) and B (xb; yb) on the 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) = 12.
Since MN = NK ≠ MK, this triangle MNK is an isosceles triangle.
Answer: Triangle MNK is an isosceles triangle.