Question

the point which lies on the perpendiculare bisec-
tore of the line segment Joining the points
P(-3, 2) and B (11,-8) is​

Answer 1

The perpendicular bisector is the line perpendicular to the line segment passing through the midpoint of the line segment

P(−2,0)≡(x

1

,y

1

) and Q(2,5)≡(x

2

,y

2

)

Slope of PQ=

x

2

−x

1

y

2

−y

1

Slope of PQ=

2+2

5−0

=

4

5

Slope of PQ×Slope of perpendicular bisector=−1

⇒Slope of perpendicular bisector m=

5

−4

Midpoint of PQ=(0,

2

5

)≡(x

1

,y

1

)

⇒equation of PQ:y−

2

5

=

5

−4

(x−0).........................Using formula y−y

1

=m(x−x

1

)

⇒8x+10y=25 is the equation of the perpendicular bisector

On substituting first point (0,

10

25

) the equation gets satisfied.