A farmer is installing a fence. The coordinates of the vertices of the fence are A(2,2), B(2,6), C(8,6), D(8,2). If each grid square has length of 9 yards, how much wire is needed for the fence?
If you plot the points you will get a rectangle of length 6 and height of 4
so the perimeter is 12 + 8 or 20 units
take over
Too get this answer is you add six and four which get 12 and then you add eight which is 20 so 20 is your answer
20 is your answer
20 yards is the answer
You have to do 16-4 then 6-2 add the answers (20) you multiply 20 by 9 to get 180 since each grid square is 9 yards
To find the length of the fence, we need to calculate the distance between each pair of consecutive vertices (A to B, B to C, C to D, and D to A) and then add up these distances.
To calculate the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, we use the distance formula:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Let's calculate the distance between each pair of points:
Distance AB:
A(2,2) and B(2,6)
DistanceAB = √[(2 - 2)² + (6 - 2)²]
= √[(0)² + (4)²]
= √(0 + 16)
= √16
= 4 yards
Distance BC:
B(2,6) and C(8,6)
DistanceBC = √[(8 - 2)² + (6 - 6)²]
= √[(6)² + (0)²]
= √(36 + 0)
= √36
= 6 yards
Distance CD:
C(8,6) and D(8,2)
DistanceCD = √[(8 - 8)² + (2 - 6)²]
= √[(0)² + (-4)²]
= √(0 + 16)
= √16
= 4 yards
Distance DA:
D(8,2) and A(2,2)
DistanceDA = √[(2 - 8)² + (2 - 2)²]
= √[(-6)² + (0)²]
= √(36 + 0)
= √36
= 6 yards
Now, let's add up the distances to find the total length of the fence:
Total length = DistanceAB + DistanceBC + DistanceCD + DistanceDA
= 4 + 6 + 4 + 6
= 20 yards
Therefore, the farmer needs 20 yards of wire to install the fence.