A square on a coordinate plane have vertices at (3, -5) and (3, 2). what is the perimeter of the square
if the vertices are on adjacent corners, the perimeter is ... 4 (2 - -5)
if the vertices are diagonally opposite, the perimeter is ... 2 √2 (2 - -5)
36 units
To find the perimeter of a square, we need to determine the length of one side and then multiply it by 4 since all sides of a square are equal in length.
Let's find the length of one side. We can use the distance formula, which is:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
In this case, the coordinates of the vertices of the square are (3, -5) and (3, 2).
Let's denote the coordinates of the first vertex as (x₁, y₁) and the coordinates of the second vertex as (x₂, y₂).
So, x₁ = 3, y₁ = -5, x₂ = 3, and y₂ = 2.
Using the distance formula, we can find the length of the side:
Distance = √[(3 - 3)² + (2 - (-5))²]
= √[0² + 7²]
= √[0 + 49]
= √49
= 7
Therefore, the length of one side of the square is 7 units.
To find the perimeter, we multiply the length of one side by 4:
Perimeter = 7 × 4
= 28
So, the perimeter of the square is 28 units.