Final answer:
To find the area and perimeter of a square, calculate the length of the diagonal using the distance formula. Then, divide the diagonal by sqrt(2) to find the side length. Finally, use the side length to find the area and perimeter of the square.
Step-by-step explanation:
To find the area and perimeter of a square, we need to know the length of one of its sides. Since the given points (-4, 3) and (2, -3) represent the endpoints of a diagonal, we can calculate the length of the diagonal using the distance formula. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values from the given points:
d = sqrt((2 - (-4))^2 + (-3 - 3)^2) = sqrt(6^2 + (-6)^2) = sqrt(36 + 36) = sqrt(72) = 6sqrt(2)
Since the diagonal of a square is equal to the side length times the square root of 2, we can find the side length of the square by dividing the diagonal by sqrt(2).
Side length = diagonal / sqrt(2) = 6sqrt(2) / sqrt(2) = 6.
Now, we can find the area and perimeter of the square:
Area = side length^2 = 6^2 = 36
Perimeter = 4 * side length = 4 * 6 = 24
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