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Anastaziya [24]
3 years ago
14

The midpoint of a segment is (6,−4) and one endpoint is (13,−2). Find the coordinates of the other endpoint.

Mathematics
1 answer:
KengaRu [80]3 years ago
8 0

Answer: A. (-1, -6)

Step-by-step explanation:

Use the midpoint formula:

  • Endpoint #1 = (x₁, y₁) = (13, -2)
  • Endpoint #2 = (x₂, y₂)

midpoint = (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}) \\\\(6, -4) = (\frac{13+x_{2}}{2}, \frac{-2+y_{2}}{2})\\\\\frac{13+x_{2}}{2} =6\\\\13+x_{2}=6*2\\\\x_{2}=12-13=-1\\\\ \\ \frac{-2+y_{2}}{2}=-4\\\\-2+y_{2}=(-4)*2\\\\y_{2}=-8+2=-6\\\\\\\left \{ {{x_{2}=-1} \atop {y_{2}=-6}} \right.

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Answer:

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Step-by-step explanation:

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3 years ago
Type the correct answer in each box
Luba_88 [7]

Answer:

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We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :

1 - We first group terms with the same variable :

(x²+8x) + (y²+22y) + 37 = 0

2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)

(x²+8x) + (y²+22y) = - 37

3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.

x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²

y²+22y = (y²+22y+11²)-11² = (y+11)²-11²

4 - We plug the new values inside our equation :

(x+4)² - 4² + (y+22)² - 11² = -37

(x+4)² + (y+22)² = -37+4²+11²

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5 - We re-write in standard form :

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5 0
3 years ago
Does the table show a direct proportional relationship? If so, what is the constant of proportionality?
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Answer:

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Step-by-step explanation:

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k = \frac{y}{x} (1)

Where:

x - Input.

y - Output.

If we know that (x_{1}, y_{1}) = (13, 45.5), (x_{2}, y_{2}) = (14, 49) and (x_{3}, y_{3}) = (15, 52.5), then the constants of proportionalities of each ordered pair are, respectively:

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k_{3} = \frac{7}{2}

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Answer:

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Step-by-step explanation:

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