Look at the square ABCD below. A(- 2, 0) B(0, 6) C(6,4) and D(4, - 2)
What is its perimeter? Explain
8sqrt(40)
• 8sqrt(10)
4sqrt(80)
4sqrt(10)
To find the perimeter of a square, you need to add up the lengths of all four sides.
The length of a side of a square can be found using the distance formula between two points in the coordinate plane: √((x2 - x1)^2 + (y2 - y1)^2)
Using the given coordinates, we can find the lengths of the sides of the square:
AB: √((0 - (-2))^2 + (6 - 0)^2) = √(2^2 + 6^2) = √(4 + 36) = √40 = 2√10
BC: √((6 - 0)^2 + (4 - 6)^2) = √(6^2 + (-2)^2) = √(36 + 4) = √40 = 2√10
CD: √((4 - 6)^2 + (-2 - 4)^2) = √((-2)^2 + (-6)^2) = √(4 + 36) = √40 = 2√10
DA: √((-2 - 4)^2 + (0 - (-2))^2) = √((-6)^2 + 2^2) = √(36 + 4) = √40 = 2√10
Adding up the lengths of the sides:
Perimeter = AB + BC + CD + DA = 2√10 + 2√10 + 2√10 + 2√10 = 8√10
Therefore, the perimeter of the square ABCD is 8√10.