Answer :
Which point lies on the perpendicular bisector of the segment with endpoints M (7,5) and N (-1, 5)?
step 1
Find the midpoint segment MN
so
the formula to calculate the midpoint between two points is equal to
[tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]substitute the given values in the formula
[tex]\begin{gathered} (\frac{7-1}{2},\frac{5+5}{2}) \\ \\ (3,5) \end{gathered}[/tex]step 2
Find the slope segment MN
m=(5-5)/(-1-7)
m=0/-8
m=0
that means
the segment MN is a horizontal line
the perpendicular line to a horizontal line is a vertical line
step 3
Find the equation of the perpendicular line
we know that
the line passes through the midpoint of segment MN
point (3,5)
therefore
the equation of the vertical line is
x=3
therefore
the answer is