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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 1 · Q23
If the points A(4, 5), B(m, 6), C(4, 3) and D(1, n) taken in this order are the vertices of a parallelogram ABCD, then find the values of m and n.
If the points A$\displaystyle (4, 5)$, B(m, $\displaystyle 6$), C$\displaystyle (4, 3)$ and D($\displaystyle 1$, n) taken in this order are the vertices of a parallelogram ABCD, then find the values of m and n.
Marking-scheme solution
Coordinates of mid-point of AC = Coordinates of mid-point of BD
\(\displaystyle \left(\frac{4+4}{2}, \frac{5+3}{2}\right)=\left(\frac{1+\mathrm{m}}{2}, \frac{\mathrm{n}+6}{2}\right)\)
\(\displaystyle \mathrm{m}=7\)
\(\displaystyle \mathrm{n}=2\)
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