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3 years ago

Compute the perimeter of the rectangle using the distance formula. (round to the nearest integer)

Mathematics

2 answers:

GenaCL600 [577]3 years ago

5 0

The answer is D 45.
Using the distance formula and the ordered pairs (1,8) & (4,5) for the short side and ((4,5) & (17,18) for the long side.
sqrt [(x2-x2)^2 + (y2-y1)^2]
sqrt [(4-1)^2 + (5-8)^2] = sqrt [ 9 + 9 ] = sqrt (18) (short side)
sqrt [(17-4)^2 + (18-5)^1 = sqrt [169 + 169] = sqrt (338) long side
P = 2L + 2W
P = 2sqrt18 + 2sqrt 338 = 45.25 = 45

Nuetrik [128]3 years ago

4 0

You have to take the sum of the distance between each point. It doesn't matter what order you use just keep it consistent, the shortest distance between any 2 points in the plane is a straight line.

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Sindrei [870]

Answer:

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Step-by-step explanation:

Sometimes the easiest way to work these problems is to get a little help from technology. The GeoGebra program/app can tell you the length of a "polyline", but it takes an extra segment to complete the perimeter. It shows the perimeter to be ...

14.87 + 2 = 16.87 ≈ 16.9 . . . units

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The distance formula can be used to find the lengths of individual segments. It tells you ...

d = √((Δx)² +(Δy)²)

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EA = Δy = 2

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3 years ago

Verify the pythagorean identity 1 + c o t ^2 θ = c s c ^2 θ

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Answer: The identity is verified. See the explanation.

Step-by-step explanation:

You must keep on mind the following identities:

$csc\theta=\frac{cos\theta}{sin\theta}\\\\csc\theta=\frac{1}{sin\theta}\\\\sin^2\theta+cos^2\theta=1$

Therefore, by substitution, you can rewrite the identity as shown below:

$1+cot^2\theta=csc^2\theta\\\\1+\frac{cos^2\theta}{sin^2\theta}=csc^2\theta$

Simpliying, you obtain:

$\frac{sin^2\theta+cos^2\theta}{sin^2\theta}=csc^2\theta\\\\\frac{1}{sin^2\theta}=csc^2\theta\\\\csc^2\theta=csc^2\theta$

The identity is verified.

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