Question

The line segment joining the points 3,-4 and 1,2 is trisected at the points P and Q . if the coordinates of P and Q are p,-2 and 5/3 , q Respectively, then find the values of P nd Q

Answer 1

Answer→

Coordinates of P( 7/3 , - 2 ) and Q ( 5/3 , 0 )

Solution→

Given -

Coordinates of P(p,-2)

Coordinates of Q(5/3,q)

→ Let the coordinates A(3,-4) and B(1,2)

Now as given that P and Q trisect AB , So

AP = PQ = QB

It means that

AQ : QB = 2 : 1 and AP : PQ = 1 : 1

1. Here, In AQ : QB

m1 = 2 , m2 = 1 , y1 = -4 , y2 = 2

So now by internal division formula

$= > \: \frac{4 - 4}{2 + 1} = 0$

So Coordinates of Q( 5/3 , 0 )

2. In AP : PQ

By using mid point formula

y1 = -4 , y2 = 0

$= > \: \frac{ \frac{5}{3} + 3}{2} = \frac{7}{3}$

So Coordinates of P( 7/3 , -2 )