Complete Question:
The given line segment has a midpoint at (3, 1). On a coordinate plane, a line goes through (2, 4), (3, 1), and (4, -2).
What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?
Answer:
[tex]y = \frac{1}{3}x[/tex]
Step-by-step explanation:
From the question, we understand that the line goes through [tex](2, 4), (3, 1), and\ (4, -2).[/tex]
First, we calculate the slope of the above points
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (2,4)[/tex]
[tex](x_2,y_2) = (3,1)[/tex]
[tex]m = \frac{1 - 4}{3 - 2}[/tex]
[tex]m = \frac{-3}{1}[/tex]
[tex]m = -3[/tex]
Also; from the question, we understand that the line segment is perpendicular to the above points.
This slope (m2) of the line segment is calculated as:
[tex]m_2 = -\frac{1}{m}[/tex]
Substitute -3 for m
[tex]m_2 = -\frac{1}{-3}[/tex]
[tex]m_2 = \frac{1}{3}[/tex]
Lastly, we calculate the equation of the line using:
[tex]y - y_1 = m_2(x - x_1)[/tex]
The line segment has a midpoint at (3, 1)
So:
[tex]y - 1 = \frac{1}{3}(x - 3)[/tex]
Open bracket
[tex]y - 1 = \frac{1}{3}x - 1[/tex]
Add 1 to both sides
[tex]y - 1 +1= \frac{1}{3}x - 1+1[/tex]
[tex]y = \frac{1}{3}x[/tex]
Hence, the equation of the line segment is: [tex]y = \frac{1}{3}x[/tex]
Answer:
A. y = One-thirdx
Step-by-step explanation:
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