Find an equation for the perpendicular bisector of the line segment whose endpoints
e (-3, -8) and (5,-4).
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Step-by-step explanation:

Perpendicular Bisector

The bisector of a segment defined by points (x1,y1) and (x2,y2) must pass by the midpoint of the segment.

The midpoint (xm,ym) is calculated as follows:

The endpoints of the segment are (-3,-8) and (5,-4), thus the midpoint M is:

Midpoint: M(1,-6)

Let's find the slope of the given segment. The slope can be calculated with the formula:

If the bisector is also perpendicular, its slope m2 and the slope of the segment m1 must comply:

Solving for m2:

Once we have the slope -2 and the point through which our line must pass (1,-6), we compute the equation in its point-slope form:

Operating

Rearranging

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step-by-step explanation:

the x's and the y's both go up the same amount each time, therefore it will be a linear function because it will go in a straight line when drawn on a graph.

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