suppose the endpoints of one side of a rotated square are (-5,-5) and (1,-1). Find the dimensions and area of the square
d^2 = (1+5)^2 + (-1+5)^2
d^2 = 36 + 16
d^2 = 52 = area
d = side length = sqrt(52) = 2 sqrt(13)
To find the dimensions and area of the square, we can first find the length of one side of the square using the given endpoints.
The length of a side of the square is the distance between the two endpoints of that side. We can use the distance formula to calculate this distance:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's label the coordinates of the endpoints as follows:
Endpoint 1: (-5, -5)
Endpoint 2: (1, -1)
Using the distance formula, we can calculate the distance between these two points:
Distance = √((1 - (-5))^2 + (-1 - (-5))^2)
= √((1 + 5)^2 + (-1 + 5)^2)
= √(6^2 + 4^2)
= √(36 + 16)
= √52
Now that we have the length of one side of the square, we can find its dimensions and area.
Since all sides of a square have the same length, the dimensions of the square are equal. Let's label the length of one side of the square as 's'.
s = √52
Therefore, the dimensions of the square are s x s.
Dimensions = √52 x √52 = √(52 x 52) = 52
The area of a square is calculated by squaring the length of one of its sides:
Area = s^2 = (√52)^2 = 52
So, the dimensions of the square are 52 x 52 units, and its area is 52 square units.