Coordinate Geometry
CH07 Question Bank
CBSE_CH07_QUESTION_BANK
Grade 10
Question:
If $(a,b)$ is the midpoint of the line segment joining $(10,-6)$ and $(k,4)$, and $a-2b=18$, find the value of $k$.
Step-by-Step Solution
Key Concept: Express a and b using the midpoint formula in terms of k, then substitute into the given condition.
$a=\dfrac{10+k}{2}$, $b=\dfrac{-6+4}{2}=-1$. [1.0 Mark]
Substituting into $a-2b=18$: $\dfrac{10+k}{2}-2(-1)=18\Rightarrow\dfrac{10+k}{2}=16$. [1.0 Mark]
$10+k=32\Rightarrow k=22$. [1.0 Mark]
Correct Answer:
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