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Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
Find the ratio in which the point $P(x,y)$ divides the line segment joining $A(1,-5)$ and $B(-4,5)$, given that $P$ lies on the $x$-axis. Also find the coordinates of $P$.
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, then find x.
Let $P$ divide $AB$ in the ratio $k:1$. Since $P$ lies on the $x$-axis, its $y$-coordinate is $0$: $0=\dfrac{5k+(-5)(1)}{k+1}$. [1.5 Marks]
$5k-5=0\Rightarrow k=1$. So the ratio is $1:1$, meaning $P$ is the midpoint of $AB$. [1.5 Marks]
$x$-coordinate: $x=\dfrac{1(-4)+1(1)}{1+1}=\dfrac{-3}{2}$. So $P=\left(-\dfrac32,0\right)$. [2.0 Marks]
Correct Answer:
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