Question

Nov 30, 4:58:43 PMWatch help videoFind an equation for the perpendicular bisector of the line segment whose endpointsare (2,7) and (-6,3).Answer:Submit Answerattempt i out of 3 / problem 1 out of max 1Privacy Policy Terms of ServiceCopyright 2020 DeltaMath.com. All Rights Reserved

Answer 1

A bisector is a line that divides the figure ins two equal parts.

With this in mind the bisector of the line with endpoints (2,7) and (-6,3) has to pass in the middle point of those points. To find the middle point we need to use the formula:

$(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})$

Therefore the middle point of the segment is:

$(\frac{2+(-6)}{2},\frac{7+3}{2})=(\frac{-4}{2},\frac{10}{2})=(-2,5)$

Hence, the bisector line will pass through the point (-2,5).

Now we need to find the slope of the bisector line. We know that this has to be perpendicular to the line segment (2,7) and (-6,3). The slope of the original segment is given by:

$m=\frac{3-7}{-6-2}=\frac{-4}{-8}=\frac{1}{2}$

Now, we know that two lines are perpendicular if and only if:

$m_1m_2=-1$

Then, the bisector will have slope:

$\begin{gathered} \frac{1}{2}m_2=-1 \\ m_2=-2 \end{gathered}$

Now that we have the slope and a point of the bisector we can use the equation of the line:

$y-y_1=m(x-x_1)$

Then:

$\begin{gathered} y-5=-2(x-(-2)) \\ y-5=-2(x+2) \\ y-5=-2x-4 \\ y=-2x-4+5 \\ y=-2x+1 \end{gathered}$

Therefore the equation of the perpendicular bisector is:

$y=-2x+1$