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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 2 · Set 1 · Q28
If the mid-point of the line segment joining the points A (3,4) and B ( k, 6) is P ( x, y ) and x + y -10=0, then find the value of k.
If the mid-point of the line segment joining the points $\displaystyle \mathrm{A}(3,4)$ and $\displaystyle \mathrm{B}(\mathrm{k}, 6)$ is $\displaystyle \mathrm{P}(\mathrm{x}, \mathrm{y})$ and $\displaystyle \mathrm{x}+\mathrm{y}-10=0$, then find the value of k .
Marking-scheme solution
\[\begin{aligned}
& \mathrm{x}=\frac{3+\mathrm{k}}{2} \\
& \text { and } \mathrm{y}=\frac{4+6}{2}=5 \\
& \therefore\left(\frac{3+\mathrm{k}}{2}\right)+5-10=0 \\
& \Rightarrow \mathrm{k}=7
\end{aligned}
\]
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