Question

The perpendicular bisector of the line segment joining the points A(1,1) and B(3,5) cuts the x-axis at :

• A. (-4, 0)
• B. (8, 0)
• C. (4, 0)
• D. (5, 0)

Answer 1

Answer:

B. (8, 0)

Midpoint is

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

$=(\frac{1+3}{2},\frac{1+5}{2})=(2,3)$

$m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{5-1}{3-1}=\frac{4}{2}=2$

$m_1 \times m_2=-1$

$m_2=\frac{-1}{2}$

Equation of the perpendicular line is

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

$m_2=\frac{-1}{2}, (x_1,y_1)=(2,3)$

$y-3=\frac{-1}{2}(x-2)$

$2y-6=-x+2$

$2y-6+x-2=0$

$x+2y-8=0$

= (8,0)