Given a rhombus with diagonals of 8 cm and 12 cm, it is known that the diagonals

Given a rhombus with diagonals of 8 cm and 12 cm, it is known that the diagonals of the rhombus lie on the coordinate axes. Find the coordinates of the vertices of the rhombus and the length of the side of the rhombus.

1. It is known that the diagonals of a rhombus at the intersection point are halved.

2. If the coordinates of the point of intersection of the diagonals are (0; 0), then the vertices of the rhombus along the OX axis are equidistant from the zero point to the left and right by 4 cm, and have coordinates (-4; 0) and (4; 0).

The vertices of the rhombus lying on the OY axis are equidistant from the zero point, and have coordinates (0; 6) and (0; -6).

3. The side a of the rhombus is calculated by the Pythagorean theorem.

a ^ 2 = 4 ^ 2 + 6 ^ 2 = 16+ 36 = 52;

a = 52 ^ 2 = 2 * 13 ^ 2.

Answer: The coordinates of the vertices of the rhombus lying on the abscissa axis (-4; 0) and (4; 0).

The coordinates of the vertices of the rhombus lying on the ordinate axis (0; 6) and (0; -6).

The side length of the rhombus is 2 * 5 ^ 2.