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Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
Find the ratio in which the $x$-axis divides the line segment joining the points $(2,-3)$ and $(5,6)$. Also find the coordinates of the point of division.
Step-by-Step Solution
Key Concept: A point on the x-axis has y-coordinate 0; use this in the section formula to find the ratio.
Let the $x$-axis divide the segment in ratio $k:1$ at the point where $y=0$: $0=\dfrac{6k-3}{k+1}\Rightarrow6k=3\Rightarrow k=\dfrac12$. [1.0 Mark]
So the ratio is $1:2$. [1.0 Mark]
$x$-coordinate of the point: $x=\dfrac{5(1)+2(2)}{1+2}=\dfrac{5+4}{3}=3$. So the point of division is $(3,0)$. [1.0 Mark]
Correct Answer:
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