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tino4ka555 [31]
3 years ago
11

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

Mathematics
2 answers:
frosja888 [35]3 years ago
7 0

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:

y = \frac{1}{3}x

Step-by-step explanation:

From the question, we understand that the line goes through (2, 4), (3, 1), and\ (4, -2).

First, we calculate the slope of the above points

m = \frac{y_2 - y_1}{x_2 - x_1}

Where

(x_1,y_1) = (2,4)

(x_2,y_2) = (3,1)

m = \frac{1 - 4}{3 - 2}

m = \frac{-3}{1}

m = -3

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:

m_2 = -\frac{1}{m}

Substitute -3 for m

m_2 = -\frac{1}{-3}

m_2 = \frac{1}{3}

Lastly, we calculate the equation of the line using:

y - y_1 = m_2(x - x_1)

The line segment has a midpoint at (3, 1)

So:

y - 1 = \frac{1}{3}(x - 3)

Open bracket

y - 1 = \frac{1}{3}x - 1

Add 1 to both sides

y - 1 +1= \frac{1}{3}x - 1+1

y = \frac{1}{3}x

Hence, the equation of the line segment is: y = \frac{1}{3}x

FinnZ [79.3K]3 years ago
5 0

Answer:

A. y = One-thirdx

Step-by-step explanation:

2020 Edge

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