Mark the vertices A (-4; 2), B (1; 7), C (6; 2) of the square ABCD on the coordinate plane. Find the coordinates of point D.

Determine which of the three sides of the triangle ABC are two adjacent sides of the square. Let’s find the lengths of the sides:

| AB | = ((1 + 4) ^ 2 + (7 – 2) ^ 2) ^ (1/2) = (25 + 25) ^ (1/2) = 50 ^ (1/2).

| BC | = ((6 – 1) ^ 2 + (2 – 7) ^ 2) ^ (1/2) = (25 + 25) ^ (1/2) = 50 ^ (1/2).

| AC | = ((6 + 4) ^ 2 + 0) ^ (1/2) = 10;

As you can see, the sides AB and BC are adjacent in a square, then the coordinates of point D will be symmetric to the coordinates of point B relative to the line y = 2.

We get the coordinates of the point: D (1; -3).