Mathematics — CBSE Class 10 board question

Let the Y-axis divide the line segment joining A(5, 3) and B(−1, 6) in the ratio k : 1.

Any point on the Y-axis has x-coordinate = 0.

Using the section formula for the x-coordinate:

$$x = \frac{k \cdot (-1) + 1 \cdot 5}{k + 1} = 0$$

$$\Rightarrow -k + 5 = 0$$

$$\Rightarrow k = 5$$

So the ratio is k : 1 = 5 : 1.

∴ The Y-axis divides the line segment joining (5, 3) and (−1, 6) in the ratio 5 : 1.

Source: Chapter 7, Section 7.3 (Section Formula)

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• A point on the Y-axis always has x-coordinate = 0. Use this fact directly with the section formula.
• Let the ratio be k : 1 (not m : n) to keep algebra simple — you only solve one equation.
• Examiners award marks for: correct setup of section formula (1 mark), correct equation and solving for k (1 mark), stating the final ratio (1 mark).
• You don't need to find the y-coordinate unless asked.