Suppose a rectangle is drawn on a coordinate plane. What is the perimeter of the rectangle if its verticies are at coordinates (1,2), (1,6), (5,6),

Question

(
1
,
2
)
,

(
1
,
6
)
,

(
5
,
6
)
,
and (5,2)
(
5
,
2
)
? Round your answer to the nearest tenth. (1 point)
The perimeter is approximately
units.

Answer 1

To find the perimeter of the rectangle given its vertices, we first need to determine the lengths of its sides.

The corners of the rectangle are:

• \( A(1, 2) \)
• \( B(1, 6) \)
• \( C(5, 6) \)
• \( D(5, 2) \)

We can find the lengths of the sides as follows:

1. Length of side AB (vertical side):

   • The y-coordinates of points A and B are 2 and 6, respectively.
   • Length \( AB = |6 - 2| = 4 \) units.

2. Length of side AD (horizontal side):

   • The x-coordinates of points A and D are both 1 and 5, respectively.
   • Length \( AD = |5 - 1| = 4 \) units.

The perimeter \( P \) of the rectangle is calculated using the formula: \[ P = 2(\text{length} + \text{width}) \] Here, the length and width are both 4 units (since \( AB = CD = 4 \) and \( AD = BC = 4 \)).

Thus, the perimeter is \[ P = 2(4 + 4) = 2 \times 8 = 16 \text{ units}. \]

So, the perimeter of the rectangle is approximately 16.0 units.