Look at the square ABCD below, A (-2,0) B(0,6) C (6,4) D(4 -2)
What is the perimeter
To find the perimeter of the square ABCD, we need to find the distance between each pair of consecutive points and then sum them up.
Using the distance formula:
Distance between points (x1, y1) and (x2, y2) is given by:
√((x2 - x1)^2 + (y2 - y1)^2)
Distance between A (-2,0) and B(0,6):
= √((0 - (-2))^2 + (6 - 0)^2)
= √(2^2 + 6^2)
= √(4 + 36)
= √40
= 2√10
Distance between B(0,6) and C(6,4):
= √((6 - 0)^2 + (4 - 6)^2)
= √(6^2 + (-2)^2)
= √(36 + 4)
= √40
= 2√10
Distance between C(6,4) and D(4,-2):
= √((4 - 6)^2 + (-2 - 4)^2)
= √((-2)^2 + (-6)^2)
= √(4 + 36)
= √40
= 2√10
Distance between D(4,-2) and A(-2,0):
= √((-2 - 4)^2 + (0 - (-2))^2)
= √((-6)^2 + 2^2)
= √(36 + 4)
= √40
= 2√10
Now, the perimeter is the sum of these distances:
Perimeter = 2√10 + 2√10 + 2√10 + 2√10
Perimeter = 8√10
Therefore, the perimeter of the square ABCD is 8√10 units.