Question

Dec 21, 8:23:34 PMWatch help videoFind an equation for the perpendicular bisector of the line segment whose endpointsare (-8, 1) and (-4, –7).Answer:Submit Answerattempt 1 out of 3 / problem 1 out of max 1Privacy Policy Terms of ServiceCopyright 2020 DeltaMath.com. All Rights Reserved.

Answer 1

First, we must find the midpoint of the given segment by means of the formula:

$(\frac{x1+x2}{2},\frac{y1+y2}{2})$

Where (x1,y1) and (x2,y2) are the endpoints of the line segment.

in this case, we get:

$(\frac{-8-4}{2},\frac{1-7}{2})=(\frac{-12}{2},\frac{-6}{2})=(-6,-3)$

This is the point at which the segment will be bisected.

Now, we need to find the slope of the segment that is perpendicular to the existing line, to do this, we use the formula of the slope m:

$m=\frac{y2-y1}{x2-x1}=\frac{-7-1}{-4-(-8)}=\frac{-8}{4}=-2$

Since the bisector is perpendicular to this line, its slope is the opposite and reciprocal of -2, which is:

$-\frac{1}{-2}=\frac{1}{2}$

Now we know that the bisector has a slope equals 1/2 and that it goes through the point (-6,-3).

We can replace these values into the equation y=mx+b, which represents a line whose slope is m and its intercept is b, we can solve for b, like this:

$\begin{gathered} -3=\frac{1}{2}(-6)+b \\ -3=-3+b \\ -3+3=-3+3+b \\ 0=b \\ b=0 \end{gathered}$

Then, the equation of the bisector is:

$y=\frac{1}{2}x$