Question

If P, Q are the points of trisection of A(1,-2)B(-5,6) then PQ=​

Answer 1

The required value of PQ is $\sqrt{13}$

Step-by-step explanation:

Given : A(1,-2) and B(-5,6)

A----------P---------Q-----------B

According to the given condition

AP=PQ=QB

So, P divide AB in the ratio 1:2

Let the co ordinates of P be (x,y)

x=[1 x(-7)+2 x 2]/(2+1)=-3/3=-1

y=[1 x 4+2 x (-2)]/(2+1)=0

So the coordinates of P are (-1,0)

Again Q divides AB in the ration 2:1

Let the co ordinates of Q be (a,b)

a=[2 x(-7)+1 x 2]/(2+1)=-12/3=-4

b=[2 x 4+1 x (-2)]/(2+1)=2

So the coordinates of Q are (-4,2)

Hence PQ= sqrt[{-1-(-4)}^2 + (0-2)^2}

=sqrt(9+4) =sqrt(13)