Final answer:
To determine whether the points A(-2,3), B(2,2), C(1,-2), and D(-3,-1) form a rectangle, a rhombus, or a square, we need to consider their properties such as slopes and lengths. By calculating slopes and lengths, we can determine the shape formed by the points.
Step-by-step explanation:
To determine whether the points A(-2,3), B(2,2), C(1,-2), and D(-3,-1) form a rectangle, a rhombus, or a square, we need to consider their properties.
1. Rectangle: A rectangle is a quadrilateral with four right angles. To check if the given points form a rectangle, we can calculate the slopes of the sides AB, BC, CD, and DA. If any pair of opposite sides have slopes that are negative reciprocals of each other (i.e., their product is -1), then the shape is a rectangle.
2. Rhombus: A rhombus is a quadrilateral with all sides of equal length. To check if the given points form a rhombus, we can calculate the lengths of the sides AB, BC, CD, and DA. If all four sides have the same length, then the shape is a rhombus.
3. Square: A square is a quadrilateral with four right angles and all sides of equal length. To check if the given points form a square, we can apply the same conditions as for a rectangle and a rhombus. The slopes of opposite sides must be negative reciprocals of each other, and all four sides must have the same length.
By calculating slopes and lengths, we can determine whether the given points form a rectangle, a rhombus, or a square.