Find the coordinates of the vertex D of the rectangle ABCD by the coordinates of its vertex:

Find the coordinates of the vertex D of the rectangle ABCD by the coordinates of its vertex: A (1; 1), B (1; 5) C (7; 5) Calculate the perimeter of the given rectangle in unit segments

The easiest way is to find the missing vertex graphically. Let us denote the known vertices of the rectangle on the coordinate plane. Let’s finish the figure to get a four-sided square, the sides intersect at right angles, and the opposite sides are parallel. We also graphically find the coordinates of the point D (7; 1).
The perimeter is the sum of all sides. But we do not know the lengths of the sides, but only the coordinates of the vertices. In our case, the sides of the quadrilateral are parallel to the axes of the coordinate plane. This means that the coordinates of neighboring vertices will have one common coordinate and differ in the second. The difference between the larger and smaller coordinates at the adjacent vertices will be the length of the corresponding side.
BC = AD = 7 – 1 = 6;
AB = CD = 5 – 1 = 4.
P = BC + CD + DA + AB = 6 + 4 + 6 + 4 = 20.
Answer: D (7; 1); P = 20.