Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
Find the ratio in which the point $(-1,6)$ divides the line segment joining $(-3,10)$ and $(6,-8)$.
Step-by-Step Solution
Key Concept: Let the ratio be k:1 and set up the section formula equation for either coordinate.
Let the ratio be $k:1$. Using the $x$-coordinate: $-1=\dfrac{6k-3}{k+1}\Rightarrow-k-1=6k-3$. [1.0 Mark]
$-7k=-2\Rightarrow k=\dfrac27$. [1.0 Mark]
So the ratio is $2:7$. Verification with $y$: $y=\dfrac{-8(2)+10(7)}{2+7}=\dfrac{-16+70}{9}=\dfrac{54}{9}=6$ ✓, matching the given point. [1.0 Mark]
Correct Answer:
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