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stiv31 [10]
3 years ago
14

Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)

Mathematics
1 answer:
Sedbober [7]3 years ago
6 0

Answer:   \bold{y=-\dfrac{1}{3}x-1}

<u>Step-by-step explanation:</u>

(4, 1) & (2, -5)

First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\

Next, find the midpoint of (4, 1) and (2, -5):

Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

y - y_1 = m_{\perp}(x - x_1)\\\\y - (-2) = -\dfrac{1}{3}(x - 3)\\\\y + 2=-\dfrac{1}{3}x +1\\\\y =-\dfrac{1}{3}x - 1\\


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Hope this helps! Please mark brainliest! Have a great day!



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<span>Dr. Graham currently has two acid solutions.
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Dr. Graham needs 30 L of a 50% acid solution
We set up 2 equations in which s = 60% acid and t = 20% acid
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So, she needs to mix 22.5 liters of 60% acid with 7.5 liters of 20% acid.

Source:
http://1728.org/mixture.htm


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