Question

The line segment joining of the points A(3, −4)and B(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, find the values of
p and q.

Answer 1

Answer:

We are given with line segment joining the points A(1,−2),B(−3,4)

Let P and Q be the points of trisection of AB i.e., AP=PQ=QB

Therefore, P divides AB internally in the ratio 1:2

Therefore, the coordinates of p, by applying the section formula, are

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

=

1+2

1(−3)+2(1)

,

1+2

1(4)+2(−2)

=

3

–1

,0

Now, q also divides AB internally in the ratio 2:1. So, the coordinates of q are

=

1+2

2(−3)+1(1)

,

1+2

2(4)+1(−2)

=

3

–5

,

3

4

Therefore, the coordinates of the points of trisection of the line segment joining A and B are

(

3

–1

,0),(

3

–5

,

3

4

)