The endpoints of a diagonal of a square are (-2,2) and (1,5). What is the area of the square?
find the distance between the two points, as usual.
Now, since the area of a square is
a = d^2/2, just figure that.
To find the area of a square, we need to know the length of one side. In this case, we can use the distance formula to find the length of the diagonal and then divide it by √2 to get the length of a side.
Step 1: Find the length of the diagonal
The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Using the given points (-2,2) and (1,5), we can calculate the length of the diagonal:
d = √((1 - (-2))² + (5 - 2)²)
= √(3² + 3²)
= √(9 + 9)
= √18
Step 2: Find the length of one side
To get the length of one side of the square, we divide the length of the diagonal by √2:
s = √18 / √2
Step 3: Calculate the area of the square
The area of a square is given by the formula:
A = s²
Substituting the length of the side we found in step 2:
A = (√18 / √2)²
= (18/2)
= 9
Therefore, the area of the square is 9 square units.
To find the area of a square, we need to know the length of its side.
In this case, we are given the endpoints of a diagonal. We can use the distance formula to find the length of the diagonal, and then use that to calculate the side length of the square.
The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula:
distance = sqrt((x2-x1)^2 + (y2-y1)^2)
Let's calculate the length of the diagonal using the given endpoints:
distance = sqrt((1-(-2))^2 + (5-2)^2)
= sqrt(3^2 + 3^2)
= sqrt(9 + 9)
= sqrt(18)
= 3sqrt(2)
Since the diagonal of a square forms an isosceles right triangle with two sides of equal length, we can use the Pythagorean theorem to find the length of the square's side. In a square, the length of the diagonal (d) is related to the length of the side (s) by the equation:
d = sqrt(2) * s
Let's solve for s, the side length of the square:
3sqrt(2) = sqrt(2) * s
Dividing both sides by sqrt(2), we get:
s = 3
Now that we know the length of the side of the square, we can calculate its area. The area of a square is given by the formula:
area = side length^2
Plugging in the value for the side length, we get:
area = 3^2
= 9
Therefore, the area of the square is 9 square units.