Q)  Find the coordinates of the points of trisection of the line segment joining the points A(- 1, 4) and B(- 3, – 2)

(Q 30 – 30/2/2 – CBSE 2026 Question Paper)

Ans: 

Step 1: Since, A Trisection means dividing a line segment into three equal parts.

It means, if AB is a line, then P and Q are two points on AB, such that:

AP = PQ = QB

∴ we can say that P divides the line AB in 1 : 2

Similarly, we can say that Q divides the line AB in 2 : 1

Step 2: We know that the coordinates of a point, dividing the line, in ration m:n, is given by

From 1st condition, P divides line AB in ration of 1 : 2

Here, coordinates of point A are (- 1, 4) and B (- 3, – 2)

∴ coordinates of a point P, are:

=

=

=

Step 3: From 2nd condition, Q divides line AB in ration of 2 : 1,

Here, coordinates of point A are (- 1, 4) and B (- 3, – 2)

∴ coordinates of a point Q, are:

=

=

=

Therefore, the coordinates of the points are and . 

Step 4: (if asked to plot, then) when we plot this line and the trisection points, P and Q, we get this diagram:

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