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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 2 · Set 2 · Q27
If (a, b) is the mid-point of the line segment joining the points A(10, - 6) and B ( k, 4) and a -2 b =18, then find the value of k.
If (a, b) is the mid-point of the line segment joining the points A$\displaystyle (10, - 6)$ and $\displaystyle \mathrm{B}(\mathrm{k}, 4)$ and $\displaystyle \mathrm{a}-2 \mathrm{~b}=18$, then find the value of k .
Marking-scheme solution
\[\begin{aligned}
& \quad a=\frac{10+k}{2} \\
& \text { and } b=\frac{-6+4}{2}=-1 \\
& \text { Given, } a-2 b=18 \\
& \Rightarrow \frac{10+k}{2}-2(-1)=18 \\
& \Rightarrow k=22
\end{aligned}
\]
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