By using distance formula we can find the type of figure as -
if by using distance formula if all sides are equal the shape is square or rhombus.
2 if opposite sides are equal then the shape is rectangle or a parallelogram.

Using Distance Formula to Find the Type of Figure Formed by Four Points

Finding the type of figure formed by four points using the distance formula involves determining the lengths of the sides of the figure and analyzing these lengths to classify the figure. Below are the steps to do this:

1. Identify the Four Points
- Begin by identifying the coordinates of the four points given in the problem. For example, let's say the points are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4).

2. Calculate the Distances between the Points
- Use the distance formula to calculate the distances between each pair of points. The distance formula is √[(x2 - x1)^2 + (y2 - y1)^2].
- Calculate the distances AB, AC, AD, BC, BD, and CD.

3. Analyze the Lengths of the Sides
- Once you have calculated the distances, compare them to determine the type of figure formed by the four points.
- If all sides are equal, the figure is a square.
- If opposite sides are equal and parallel, the figure is a parallelogram.
- If all sides are of different lengths, the figure is a quadrilateral.

4. Classify the Figure
- Based on the lengths of the sides, classify the figure as a square, parallelogram, quadrilateral, or any other specific type if applicable.

By following these steps and using the distance formula to calculate the lengths of the sides, you can determine the type of figure formed by four points accurately.