The bisector AK is drawn in the triangle ABC. Find the coordinates of point K, if A (-1; 2) B (8; 6) C (2; -2).

Since we have the coordinates of all points, we can find the length of the segment CB, which is the side of the triangle ABC and is divided into equal parts by the bisector AK with point K.
Let’s find the length of the side CB:
CB = √ (6 ^ 2 + 8 ^ 2) = √ (36 + 64) = √100 = 10.
The segments CK and KC are equal to each other and equal to 10: 2 = 5.
Find the coordinates of the point K:
On the coordinate line Ox, point C takes the value 2, and point B – 8. Then the middle of this segment takes the value x = 2 + (6: 2) = 2 + 3 = 5.
On the coordinate line Oy, point C takes the value – 2, and point B – 6. Then the middle of this segment will take the value y = – 2 + (8: 2) = – 2 + 4 = 2.
ANSWER: point K has coordinates (5, 2).