Question

Prove that the given points taken in order are the vertices of a square,(4,3), (2, 1), (4.-1), (6, 1)​

Answer 1

To prove that the given points are the vertices of a square, we need to show that the distances between each pair of consecutive points are equal and that the angles between them are all right angles.

Step-by-step explanation:

To prove that the given points are the vertices of a square, we need to show that the distances between each pair of consecutive points are equal and that the angles between them are all right angles.

1. Calculate the distance between (4, 3) and (2, 1) using the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2). In this case, d = sqrt((2 - 4)^2 + (1 - 3)^2) = 2 * sqrt(2).
2. Next, calculate the distance between (2, 1) and (4, -1) and verify that it is equal to 2 * sqrt(2).
3. Similarly, calculate the distance between (4, -1) and (6, 1) and confirm that it is 2 * sqrt(2).
4. Finally, calculate the distance between (6, 1) and (4, 3) and ensure that it is also 2 * sqrt(2).

Since all the distances between consecutive points are equal, the given points are the vertices of a square.