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.
Look at the square ABCD below, A (-2,0) B(0,6) C (6,4) D(4 -2)
What is the perimeter
1 answer