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4 years ago

The line that is the perpendicular bisector of the segment whose endpoints are R(-1,6) and (5,5)

Mathematics

1 answer:

Oksi-84 [34.3K]4 years ago

6 0

Answer:

First find midpoint: \left( \frac{-1+5}{2}, \frac{6+5}{2}\right) = (2, 5.5)

Find slope of line that passes through R and S: slope = \frac{6-5}{-1-5} = \frac{-1}{6}

Negative reciprocal of slope to get slope of perpendicular: new slope = 6

Line will be: y-5.5=6(x-2)

y = 6x - 6.5

Step-by-step explanation:

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Divide both sides by the number of the right side so the right side equals 1:

$\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}$

Simplify:

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center = (1, 2)
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co-vertices = (1, 0) and (1, 4)
$\textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}$
$\textsf{Foci}: \quad (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)$

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