Question

The vertices of YEAR are Y(1,-4) E(3,0), A (-1,2) and R( -3,-2) . prove that YEAR is a Square

Answer 1

To prove that YEAR is a square, we need to show that all four sides have the same length and all four angles are right angles (90 degrees).

Side Lengths: To find the lengths of the sides, we can use the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

For example, to find the length of the side that connects Y and E, we can use the following calculation:

d = √((3 - 1)² + (0 - (-4))²) = √((2)² + (4)²) = √(4 + 16) = √20

We can use the same formula to calculate the lengths of the other sides. By doing so, we will find that the length of all four sides are the same, which is √20. This means that all four sides of YEAR are congruent, and therefore it is a square.