Question

find an equation for the perpendicular bisector of the line segment whose endpoints are (9,-5) and (-5,-1)

Answer 1

The equation y = (13 / 4) · x - 19 / 2 represents the perpendicular bisector of the line segment.

How to find the equation for the perpendicular bisector of a line segment

In this problem we need to determine the equation of the line perpendicular to a line segment whose endpoints are known. The equation of the line is represented by a first grade polynomial of the form:

y = m · x + b

Where:

• m - Slope
• b - Intercept
• x - Independent variable.
• y - Dependent variable.

And the relationship between the slopes of two perpendicular lines:

m · m' = - 1

Where:

• m - Slope of the original line.
• m' - Slope of the perpendicular line.

And the slope of the original line can be found by the secant line formula:

m = Δy / Δx

And the midpoint of a line segment between two endpoints is defined below, necessary for the location of the bisector:

M(x, y) = 0.5 · A(x, y) + B(x, y)

Where:

• M(x, y) - Midpoint
• A(x, y), B(x, y) - Endpoints

First, find the slope of the line segment by secant line formula:

m = [- 1 - (- 5)] / (- 5 - 9)

m = - 4 / 13

Second, find the slope of the perpendicular bisector by the slope relationship between two perpendicular lines:

m' = - 1 / m

m' = - 1 / (- 4 / 13)

m' = 13 / 4

Third, determine the midpoint of the line segment by the midpoint formula:

M(x, y) = 0.5 · (9, - 5) + 0.5 · (- 5, - 1)

M(x, y) = (4.5, - 2.5) + (- 2.5, - 0.5)

M(x, y) = (2, - 3)

Fourth, find the intercept of the perpendicular bisector by means of the equation of the line:

b = y - m' · x

b = - 3 - (13 / 4) · 2

b = - 3 - 26 / 4

b = - 3 - 13 / 2

b = - 19 / 2

The equation for the perpendicular bisector is y = (13 / 4) · x - 19 / 2.

To learn more on perpendicular bisectors: brainly.com/question/11900712

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