CBSE 2025 · Region 3 · Set 1 · Q26 · 3 marks
If the mid-point of the line segment joining the points A$\displaystyle (3, 4)$ and $\displaystyle \mathrm{B}(\mathrm{k}, 6)$ is $\displaystyle \mathrm{P}(\mathrm{x}, \mathrm{y})$ and $\displaystyle \mathrm{x}+\mathrm{y}-10=0$, find the value of k .Find the coordinates of the points which divide the line segment joining $\displaystyle \mathrm{A}(-2,2)$ and $\displaystyle \mathrm{B}(2,8)$ into four equal parts.
If the mid-point of the line segment joining the points A$\displaystyle (3, 4)$ and $\displaystyle \mathrm{B}(\mathrm{k}, 6)$ is $\displaystyle \mathrm{P}(\mathrm{x}, \mathrm{y})$ and $\displaystyle \mathrm{x}+\mathrm{y}-10=0$, find the value of k .
Find the coordinates of the points which divide the line segment joining $\displaystyle \mathrm{A}(-2,2)$ and $\displaystyle \mathrm{B}(2,8)$ into four equal parts.
Marking-scheme solution
(a)
\[\begin{aligned}
& \mathrm{P}(\mathrm{x}, \mathrm{y}) \text { is the mid - point } \\
& \therefore(\mathrm{x}, \mathrm{y})=\left(\frac{3+\mathrm{k}}{2}, \frac{4+6}{2}\right) \\
& \mathrm{x}=\frac{3+\mathrm{k}}{2}, \mathrm{y}=5 \\
& \mathrm{x}+\mathrm{y}-10=0 \\
& \frac{3+\mathrm{k}}{2}+5-10=0 \\
& \mathrm{k}=7
\end{aligned}
\]
(b)
B \(\displaystyle (2,8)\)
Coordinates of mid - point Q of \(\displaystyle \mathrm{AB}=(0,5)\)
Coordinates of mid - point P of \(\displaystyle \mathrm{AQ}=\left(-1, \frac{7}{2}\right)\)
Coordinates of mid - point R of \(\displaystyle \mathrm{BQ}=\left(1, \frac{13}{2}\right)\)
Coordinate GeometryMidpoint of a Line SegmentApplyshort_answereasy
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CBSE Class 10 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.