Determine whether each set of points make a right triangle using the Pythagorean Theorem. 1. A(3 , -4) B(-4 , 3) C(0 , 0) 2. O(2 , 5) P(-1 , 3) Q(7 , 4) 3. T(1 , 1) U(3 , 3) V(5 , 1)

Answers

Answer 1

Answer:

[tex]1.\ A(3 , -4)\ B(-4 , 3)\ C(0 , 0)[/tex] -- Not right triangle

[tex]2.\ O(2 , 5)\ P(-1 , 3)\ Q(7 , 4)[/tex] -- Not right triangle

[tex]3.\ T(1 , 1)\ U(3 , 3)\ V(5 , 1)[/tex] -- Right triangle

Explanation:

Required

Determine whether the given points make a right triangle

[tex]1.\ A(3 , -4)\ B(-4 , 3)\ C(0 , 0)[/tex]

First, calculate the distance between each point using:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]AB = \sqrt{(3 - -4)^2 + (-4 - 3)^2}= \sqrt{98} = 7\sqrt 2[/tex]

[tex]BC = \sqrt{(-4 - 0)^2 + (3 - 0)^2}= \sqrt{25} = 5[/tex]

[tex]AC = \sqrt{(3 - 0)^2 + (-4 - 0)^2}= \sqrt{25} = 5[/tex]

From the above computations, the longest side is AB.

So;

[tex]AB^2 = BC^2 + AC^2[/tex] --- Test of Pythagoras

[tex](7\sqrt 2)^2 = 5^2 + 5^2[/tex]

[tex]98 = 25 + 25[/tex]

[tex]98 \ne 50[/tex]

The above points do not make a right triangle

[tex]2.\ O(2 , 5)\ P(-1 , 3)\ Q(7 , 4)[/tex]

Calculate distance

[tex]OP = \sqrt{(2 - -1)^2 + (5 - 3)^2}= \sqrt{13}[/tex]

[tex]PQ = \sqrt{(-1 -7)^2 + (3 - 4)^2}= \sqrt{65}[/tex]

[tex]OQ = \sqrt{(2 -7)^2 + (5 - 4)^2}= \sqrt{26}[/tex]

From the above computations, the longest side is PQ

So;

[tex]PQ^2 = OP^2 + OQ^2[/tex] --- Test of Pythagoras

[tex]\sqrt{65}^2 = \sqrt{13}^2 + \sqrt{26}^2[/tex]

[tex]65 = 13 + 26[/tex]

[tex]65 \ne 39[/tex]

The above points do not make a right triangle

[tex]3.\ T(1 , 1)\ U(3 , 3)\ V(5 , 1)[/tex]

Calculate distance

[tex]TU = \sqrt{(1 -3)^2 + (1 - 3)^2}= \sqrt{8} = 2\sqrt2[/tex]

[tex]UV = \sqrt{(3 -5)^2 + (1 - 3)^2}= \sqrt{8} = 2\sqrt2[/tex]

[tex]TV = \sqrt{(1 -5)^2 + (1 - 1)^2}= \sqrt{16} = 4[/tex]

From the above computations, the longest side is TV

So;

[tex]TV^2 = TU^2 + UV^2[/tex] --- Test of Pythagoras

[tex]4^2 = (2\sqrt 2)^2 +(2\sqrt 2)^2[/tex]

[tex]16 = 8 + 8[/tex]

[tex]16 = 16[/tex]

The above points not make a right triangle


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ur welcome

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Answer:

destructive

Explanation:

Nationalism promotes the ideas of the nation in question and is has been called loyalism. However, its is different from patriotism as patriotism is a strong connection and support for ones country. Nationalism is supporting your country to the point you care about your country more than the people around you. In nationalism, the country is not questioned it is just supported by others.

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Answers

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Answers

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Answer: Deforestation

Explanation:

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Explanation:Deforestation is the permanent destruction of forests in order to utilize the land or trees. Typically, deforestation is clearing a lot of trees without the intention of establishing future growth. Harvesting, forest fires, and insect infestations do not count as deforestation because the affected areas will eventually grow back.

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Answer:

a mass pro-democracy protest against the Chinese government.

Explanation:

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I remember learning about this and I think it is b

hello please help i’ll give brainliest

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Answer:

I think it is Runoff.

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Runoff involves using gravity to travel in the ocean.

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Answer:

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Give me a little bit and I will have one for you

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Answer:

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It forms in layers as it does on earth. Also, it was on Study Island and that was the right answer.

The correct option is D.

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Learn more about soil layers here https://brainly.com/question/23437558

#SPJ2

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i don't know what else to put

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The real question is...can a box match?

  ............................................................................................................................................                                                                                                                                        No but a tin can.

............................................................................................................................................

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Answers

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Temperature inversion usually occurs when warm air, which is lighter than cold air, moves above cold air and traps it by acting as a sort of lid over it.

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Answers

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Answer:

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4. Topography

5. Time

Pls mark as brainliest.

Answer:

Parent material

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Topography

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Answers

Answer:

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Hope it helps! Correct me if I am wrong!

I'm sure about my answer!

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Answers

Answer:

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Explanation:

hope its helpful

Answer:

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