Q) Determine the ratio in which the line 3x + y – 9 = 0 divides the line segment joining the points (1, 3) and (2, 5). Find the point of intersection.

(Q 28 – 30/3/3 – CBSE 2026 Question Paper)

Ans:

(i) calculating for division ratio

Step 1: Let’s consider the given points are A (1, 3) and B (2, 5)

Also consider that the coordinates of the inetrsection point, C is (x, y) and it divides the line segments AB in ratio of m : n.

Step 2: By section formula, we know that the coordinates of intersetion point are given by:

Here, given points are A (1, 3) and B (2, 5)

∴ Coordinates of intersetion point C =

=

=

Step 3: Since this intersetion point C also lies on line, 3 x + y – 9 = 0

Given line function is: 3 x + y – 9 = 0

∴

∴ 3 (2 m + n) + (5 m + 3 n) – 9 (m + n) = 0

∴ 6 m + 3 n + 5 m + 3 n – 9 m – 9 n = 0

∴ 2 m – 3 n = 0

∴ 2 m = 3 n

∴ m : n = 3 : 2

Therefore, the line 3x + y – 9 = 0 divides the line segment in ratio of 3 : 2.

(ii) Calculating coordinates of intersetion point

Step 4: ∵ m : n = 3 : 2

∴ we can consider m = 3 k and n = 2 k, where k is a non-zero integer

Now, we use these values of m and n to get coordinates of C

∵ Coordinates of intersetion point C =

=

=

=  =

Therefore, the coordinates of intersetion point are .

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