How can you prove a shape is a rhombus in analytical geometry
To prove that a shape is a rhombus in analytical geometry, you can use several methods:
1. Show that all four sides of the shape are equal in length: Calculate the distance between each pair of consecutive points that form the vertices of the shape using the distance formula (sqrt((x2 - x1)^2 + (y2 - y1)^2)). If all four sides are equal in length, then the shape is a rhombus.
2. Show that adjacent sides are perpendicular to each other: Calculate the slopes of the lines formed by connecting each pair of consecutive points that form the vertices of the shape. If the slopes of adjacent sides are negative reciprocals of each other (i.e., the product of the slopes is -1), then the shape is a rhombus.
3. Show that the diagonals of the shape are perpendicular to each other: Calculate the slopes of the lines formed by connecting the opposite vertices of the shape with the distance formula. If the slopes of the diagonals are negative reciprocals of each other, then the shape is a rhombus.