A rectangle is shown in the figure below. What is the perimeter? Units are in inches.

Question

points are (-3,1) (3,4) (1,1) (7,2)

(1 point)
Responses

155–√ in
155–√ in

55–√ in
55–√ in

105–√ in
105–√ in

265–√ in

Answer 1

To find the perimeter of the rectangle, we first need to determine the lengths of the sides of the rectangle using the coordinates given. However, it seems that we have points that do not clearly indicate a rectangle, as there are four arbitrary points \((-3,1)\), \((3,4)\), \((1,1)\), and \((7,2)\).

To calculate the perimeter of a rectangle, we need to establish its vertices correctly. A rectangle can be defined by two pairs of opposite vertices.

Let’s analyze the provided points:

• Points \((-3, 1)\) and \((1, 1)\) have the same \(y\)-coordinate, so they are horizontally aligned, making them potential candidates for one side of the rectangle.
• Points \((3, 4)\) and \((7, 2)\) can also potentially be aligned or serve as another pair of corners.

Assuming two pairs of vertices correspond to finding the lengths of the sides, you can calculate the length \(L\) of the sides from the x-coordinates, and width \(W\) from the y-coordinates.

1. Calculate the distance between:
   • \((-3, 1)\) and \((1, 1)\): \(L = 1 - (-3) = 1 + 3 = 4\) inches
   • \((3, 4)\) and \((7, 2)\): Using distance formula: \[ d = \sqrt{(7 - 3)^2 + (2 - 4)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \]

Assuming the lengths are given in coordinates that fit a rectangle, we could find the actual dimensions.

To compute the perimeter \(P\): \[ P = 2(L + W) \] But based on above pairs of coordinates, assuming coherence with the rectangle formula where sides perpendicular give maximum dimensions.

If the correct dimensions were received, the formula offers perimeter calculated via:

If we find lengths \(A\) and \(B\), \[ P = 2 \times (length + width) \]

Given potential responses, check each, to apply the respective dimensional outputs and check tolerability with:

• \(155 - \sqrt{\text{in}}\)
• \(55 - \sqrt{\text{in}}\)
• \(105 - \sqrt{\text{in}}\)
• \(265 - \sqrt{\text{in}}\)

Final answer determination rests on dimensional coherence, choose nearest linear adjustments to output scenarios.

To definitively calculate, ensure to analyze the points accurately regarding rectangle definition per local coordinate box obtained from vertices.

Should you need specific dimensions derived from the pair, answer accordingly.