Question

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.

Answer 1

Given:

Vertices of parallelogram ABCD are A(4, 5), B(m, 6), C(4, 3) and D(1, n).

In a parallelogram, diagonals bisect each other. So, the midpoint of diagonal AC is the same as the midpoint of diagonal BD.

Midpoint of AC:

`((4 + 4)/2, (5 + 3)/2) = (8/2, 8/2)`

= (4, 4)

Midpoint of BD:

`((m + 1)/2, (6 + n)/2)`

Equating the coordinates:

`(m + 1)/2 = 4`

⇒ m + 1 = 8

⇒ m = 7

`(6 + n)/2 = 4`

⇒ 6 + n = 8

⇒ n = 2

Values are m = 7 and n = 2.