Question

The perpendicular bisector of the line segment
joining the points A (1,5) and B (4, 6) cuts the
y-axis at
a) (0, 13)
(b) (0, -13)
c) (0,12)
(d) (13,0)​

Answer 1

answer : option (a) (0, 13)

equation of line joining the points A(1, 5) and B(4, 6) is ...

(y - 5) = (6 - 5)/(4 - 1) (x - 1)

⇒y - 5 = 1/3(x - 1)

⇒3(y - 5) = x - 1

⇒x - 3y + 14 = 0

slope of perpendicular bisector = -1/slope of AB

= -1/(1/3) = -3

now midpoint of AB = {(1 + 4)/2, (5 + 6)/2}

= {5/2 , 11/2}

so, equation of perpendicular bisector is...

(y - 11/2) = -3(x - 5/2)

⇒y + 3x - 11/2 - 15/2 = 0

⇒y + 3x - 13 = 0

so perpendicular bisector cuts the y-axis at ,

y + 3 × 0 - 13 = 0 ⇒ y = 13 i.e., (0, 13)

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