Find the coordinate of the point k which is the midpoint of the segment with ends at the points M (10,6) N (-2,4).

We need to find the coordinates of the point K, which is the midpoint of the segment with ends at the points M (10; 6) and N (-2; 4).

According to the definition, the midpoint of a line segment is a point that lies on the line segment and is equidistant from the endpoints.

To find the coordinates of the midpoint of the segment, we will use the formulas:

xk = (xm + xn) / 2;

yk = (ym + yn) / 2.

We substitute the coordinates of the ends of the segments into the formulas and calculate:

xk = (10 + (-2)) / 2 = (10 – 2) / 2 = 8/2 = 4.

yk = (6 + 4) / 2 = 10/2 = 5.

Coordinates of the point K (4; 5).

Answer: K (4; 5)