# 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.

August 29, 2021 | education

| 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).

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