Find the distance from point A (-3; 4) to the midpoint of segment BC, if B (3; 2), C (-1; 6).

We need to find the distance from point A with coordinates (-3; 4) to the middle of segment BC, if the coordinates of points B (3; 2) and C (-1; 6) are known.

First of all, we find the midpoint of the segment BC.

To do this, apply the formula:

O (x0; y0).

x0 = (x1 + x2) / 2; y0 = (y1 + y2) / 2.

We are looking for the middle of the segment:

x0 = (3 – 1) / 2 = 1; y0 = (2 + 6) / 2 = 4.

O (1; 4).

It remains to find the distance from the point with coordinates A (-3; 4) to the middle O of the segment BC:

| AO | = √ ((x2 – x1) ^ 2 – (y2 – y1) ^ 2) = √ ((1 – (-3)) ^ 2 + (4 – 4) ^ 2) = √16 = 4.