Question

The line segment joining the points P(3, 3) and Q(6, −6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

Answer 1

We have two points P (3, 3) and Q (6,−6). There are two points A and B which trisect the line segment joining P and Q.

Let the co-ordinate of A be

Now according to the section formula if any point P divides a line segment joining andin the ratio m: n internally than,

The point A is the point of trisection of the line segment PQ. So, A divides PQ in the ratio 1: 2

Now we will use section formula to find the co-ordinates of unknown point A as,

Therefore, co-ordinates of point A is(4, 0)

It is given that point A lies on the line whose equation is

So point A will satisfy this equation.

So,