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Mariana [72]
2 years ago
6

Find the distance between each pair.A ( 2, -1) B ( -6 , 5 )A.36B.120C.100

Mathematics
1 answer:
yuradex [85]2 years ago
5 0

Answer:

B. 120  and C. 100   = 0.4 DIFFERENCE Between the two pairs.

Step-by-step explanation:

2/-1 =  -2

-6/ 5 = -1.2

the difference where we divide by  /2 is -1.2 - 2 = 0.8 / 2  = 0.4

0.4 divides into all options ABC however 36 it divides 9 times

120 it divides 30 times

and 100 is divides 25 times.

9/ 0.4 = 22.5 and is wrong

30 / 0.4 = 75

25 / 0.4 = 62.5 and is wrong

therefore B 120 is correct.

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Answer:

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Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}.

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}.

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between \left(x_1, \, y_1, \, z_1\right) and \left(x_2, \, y_2, \, z_2\right) would be:

\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right).

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The equation for a sphere of radius r and center \left(x_0,\, y_0,\, z_0\right) would be:

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Expand the squares and simplify to obtain:

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