Plot and connect the points A(-4,2), B(4,2), C(4,-2), and D(-4,-2). Then, find the perimeter of rectangle ABCD.
A.
32 units
B.
20 units
C.
16 units
D.
24 units
To plot and connect the points A(-4,2), B(4,2), C(4,-2), and D(-4,-2), we first plot the points on a coordinate plane:
A(-4,2) is to the left of the y-axis at y=2.
B(4,2) is to the right of the y-axis at y=2.
C(4,-2) is to the right of the y-axis at y=-2.
D(-4,-2) is to the left of the y-axis at y=-2.
Connecting the points gives us a rectangle. To find the perimeter of the rectangle ABCD, we calculate the distance between each pair of points using the distance formula:
Distance between A(-4,2) and B(4,2):
√[(4-(-4))² + (2-2)²] = √[8² + 0] = 8 units
Distance between B(4,2) and C(4,-2):
√[(4-4)² + (2-(-2))²] = √[0 + 4²] = 4 units
Distance between C(4,-2) and D(-4,-2):
√[(-4-4)² + (-2-(-2))²] = √[(-8)² + 0] = 8 units
Distance between D(-4,-2) and A(-4,2):
√[(-4-(-4))² + (-2-2)²] = √[0 + 4²] = 4 units
Adding the distances gives us the perimeter of the rectangle ABCD:
Perimeter = 8 + 4 + 8 + 4 = 24 units
Therefore, the correct answer is D. 24 units.
A polygon has the following coordinates: A(6,-7), B(1,-7), C(1,-4), D(3,-2), E(7,-2), F(7,-4). Find the length of BC.
A.
5 units
B.
2 units
C.
3 units
D.
4 units
To find the length of BC, we calculate the distance between the points B(1,-7) and C(1,-4) using the distance formula:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(1 - 1)² + (-4 - (-7))²]
= √[0 + 3²]
= √9
= 3 units
Therefore, the correct answer is C. 3 units.