CBSE Class 10 Mathematics Standard 2024: question 26(A)

Hints

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Step-by-step solution

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1. Let $P\left(\frac{8}{5},y\right)$ divide AB, with $A(1,2)$ and $B(2,3)$, in the ratio $k:1$.

   By the section formula, the x-coordinate gives $\frac{k\cdot 2+1\cdot 1}{k+1}=\frac{8}{5}$.

   1 mark

2. Solve: $5(2k+1)=8(k+1)\Rightarrow 10k+5=8k+8\Rightarrow 2k=3\Rightarrow k=\frac{3}{2}$.

   ½ mark

3. So the required ratio is $\frac{3}{2}:1=3:2$.

   ½ mark

4. For the y-coordinate, use $m:n=3:2$:

   $y=\frac{3\times 3+2\times 2}{3+2}=\frac{13}{5}$.

   1 mark

Answer: Ratio $3:2$; $y=\frac{13}{5}$

Revise the chapter

• Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
• Topic: Section Formula (Internal Division)