Question

the line segment AB joining the points A(3,-2) and B(1,3) is trisected at the points p( a,-1/3) and Q (5/3,b) find the value of A and B

Answer 1

Answer:

a = 7/3

b= 4/3

Step-by-step explanation:

Given A (3, -2) and B(1, 3)

Also, Given that line segment joining the points A and B is trisected by the points P(a, -1/3) and Q(5/3, b)

So, P and Q are the points of trisection.

Points of trisection are those points which divide the line segment in the ration 1:2 and 2:1 internally.

Using internal sectional formula , we get

P as point that divided the segment in the ratio

1:2  internally is

(1*1 + 2*3/1+2, 3 + 2*-2/1+2)

=>P is (7/3, -1/3)

Hence by comparison with (a, -1/3), we get a =7/3.

Similarly to find Q which is the point that divided the segment in the ratio

2:1 internally is

(2*1 + 3/2+1 , 2*3 -2/2+1) which is

(5/3,4/3)

On comparison with Q(5/3, b) we get b = 4/3.