Q)  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.

(Q 25 – 30/2/2 – CBSE 2026 Question Paper)

Ans: 

We know that the in a parallelogram, the diagonals bisect each other.

It means that the midpoint of one diagonal is the same as the midpoint of the other diagonal .

Step 1: Let’s calcualte midpoint of diagonal AC

By midpoint formula, the midpoint of two points (x1, y1) and (x2,y2)
(x,y) =

∴ Midpoint of points A(4, 5) and C(4, 3)

P (x,y) =

∴ P (x,y) = (4, 4) ……………. (i)

Step 2: Let’s calcualte midpoint of diagonal BD

∴ Midpoint of points B (m, 6) and D(1, n)

P (x,y) = ……….. (ii)

Step 3: Now, since both these midpoints refer to same point

Let’s compare x – coordinates from both equations

∴ = 4

∴ (m + 1) = 8

∴ m = 7

Step 4: Similarly, we compare y – coordinates from both equations

∴ = 4

∴ (6 + n) = 8

∴ n = 2

Therefore, the values of m and n are 7 and 2 respectively.

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