Question

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

Answer 1

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: $y = \frac{1}{3}x$

Answer 2

Answer:

A. y = One-thirdx

Step-by-step explanation:

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