Question

What is the perimeter of the square formed by the vertices (0,1), (1,0), (0, -1), and (-1,0), rounded to the nearest whole unit?

a) 4 units
b) 5 units
c) 6 units
d) 8 units

Answer 1

The perimeter of the square formed by the given vertices is approximately 4.83 units, rounded to the nearest whole unit it is 5 units.

Step-by-step explanation:

The perimeter of a square can be found by adding up the lengths of all its sides. In this case, the square is formed by the vertices (0,1), (1,0), (0,-1), and (-1,0). To calculate the distance between two points, you can use the distance formula:

d = √ ((x2 - x1)² + (y2 - y1)²)

Using this formula, we can find the distance between each pair of consecutive vertices and then add them up to get the perimeter:

d1 = √ ((1 - 0)² + (0 - 1)²) = √ (1 + 1) = √2

d2 = √ ((0 - 0)² + (-1 - 0)²) = √ (0 + 1) = 1

d3 = √ ((0 - (-1))² + (-1 - 0)²) = √ (1 + 1) = √2

d4 = √ ((0 - 1)² + (0 - (-1))²) = √ (1 + 1) = √2

Now, we can add up the distances:

Perimeter = d1 + d2 + d3 + d4 = √2 + 1 + √2 + √2 ≈ 4.83

Rounding the perimeter to the nearest whole unit, we get an answer of 5 units (b).