Question

The equation of the perpendicular bisector of the line segment joining the points (1, 4) and (3, 6) is

• A. x – y – 7 = 0
• B. x + y – 7 = 0
• C. x + y + 7 = 0
• D. None of these

Answer 1

The correct option is B

x + y – 7 = 0

Let A ≡ (1, 4) and B ≡ (3, 6). Let CD be the perpendicular bisector of the line segment AB.

Now, Slope of $AB=\frac{6-4}{3-1}=1,$

$\therefore$ Slope of CD = –1 $(\because CD\perp AB)$

Since C is the mid point of AB,

$\therefore$ COOrdinates of C are $(\frac{1+3}{2},\frac{4+6}{2})or(2,5)$

$\therefore$ Equation of CD is

(y – 5) = –1(x – 2) or x + y – 7 = 0