Answer:
Option (1)
Step-by-step explanation:
Perpendicular bisector of the segment will pass through the midpoint of the segment joining two points (5, 7) and (-3, 3).
Midpoint of the segment will be,
(x, y) = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
= [tex](\frac{5-3}{2},\frac{7+3}{2})[/tex]
= (1, 5)
Slope of the line joining the given points [tex]m_1[/tex] = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_1=\frac{7-3}{5+3}[/tex]
= [tex]\frac{1}{2}[/tex]
Let the slope of the line perpendicular to the segment joining the given points is [tex]m_2[/tex].
By the property of perpendicular lines,
[tex]m_1\times m_2=-1[/tex]
[tex]\frac{1}{2}\times m_2=-1[/tex]
[tex]m_2=-2[/tex]
Since, equation of a line passing through (x', y') and slope 'm' is,
y - y' = m(x - x')
Therefore, equation of the line passing through (1, 5) and slope (-2) will be,
y - 5 = (-2)(x - 1)
y = -2x + 2 + 5
y = -2x + 7
2x + y = 7
Therefore, Option (1) will be the answer.
