Question

A(6, 1), B(8, 2) and C(9, 4) are the vertices of a parallelogram ABCD. If E is the midpoint of DC, find the area of `Delta ADE`.

Answer 1

Correct Answer - `(3)/(4)` sq unit

Let the fourth vertex be D(x, y).
Midpoint of AC is `((6+9)/(2), (4+1)/(2)), i.e., ((15)/(2), (5)/(2))`.
Midpoint of BD is `((8+x)/(2), (2+y)/(2))`
`therefore (8+x)/(2) =(15)/(2) "and" (2+y)/(2) = (5)/(2) rArr x = 7 "and" y = 3.`
So, we get the point D(7, 3).
Midpoint of DC is E`((7+9)/(2), (3+4)/(2)), i.e., E(8, (7)/(2))`
Now, A(6, 1), D(7, 3) and E`(8, (7)/(2))` are vertices of `Delta ABC.` Now find its area.