Question

Given each set of vertices, determine whether □BEFG is a rhombus, a rectangle, or a square. List all that apply. Explain. 9. B(−9,1),E(2,3),F(12,−2),G(1,−4)

Answer 1

To determine the shape of quadrilateral □BEFG, calculate the lengths of sides and slopes of opposite sides.

Step-by-step explanation:

The given set of vertices determines the coordinates of points B(-9,1), E(2,3), F(12,-2), and G(1,-4). To determine whether □BEFG is a rhombus, a rectangle, or a square, we need to check for certain properties.

1. All sides are equal: Calculate the lengths of all sides of the quadrilateral by using the distance formula. If all four sides are equal, then □BEFG is a rhombus.
2. Opposite sides are parallel: Calculate the slopes of opposite sides of the quadrilateral and check if they are equal. If they are equal, then □BEFG is a rectangle.
3. All sides are equal and opposite sides are parallel: If both conditions mentioned above are satisfied, then □BEFG is a square.

Calculate the lengths of sides, slopes of opposite sides, and determine the shape of the quadrilateral based on the given criteria.