Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
Find the ratio in which the point $(4,5)$ divides the line segment joining $(2,3)$ and $(7,8)$.
Step-by-Step Solution
Key Concept: Set up the section formula for the x-coordinate with an unknown ratio k:1, and solve for k.
Let the ratio be $k:1$. Then $4=\dfrac{7k+2}{k+1}\Rightarrow4k+4=7k+2\Rightarrow3k=2\Rightarrow k=\dfrac23$. [1.0 Mark]
So the ratio is $2:3$ (verify: $y=\dfrac{8(2)+3(3)}{5}=\dfrac{16+9}{5}=5$ ✓, matches the given point). [1.0 Mark]
Correct Answer:
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