# 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 δAde - Mathematics

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 ΔADE

#### Solution

Let  (x,y) be the coordinates of D and ( x ',y')be thee coordinates of E. since, the diagonals of a parallelogram bisect each other at the same point, therefore

(x+8)/2=(6+9)/2⇒x =7

(y+2)/2 = (1+4)/2 ⇒ y=3

Thus, the coordinates of D are ( 7,3)

E is the midpoint of DC, therefore

x' = (7+9)/2 ⇒ x' = 8

y' =(3+4)/2 ⇒ y' = 7/2

Thus, the coordinates of E are (8,7/2)

"let" A (x_1, y_1) = A(6,1) ,E (x_2,y_2) = E (8,7/2) and D(x_3,y_3) = D(7,3) Now

"Area" (Δ ABC) = 1/2 [ x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)]

=1/2[6(7/2-3)+8(3-1)+7(1-7/2)]

=1/2[3/2]

=3/4 sq. units

Hence, the area of the triangle ΔADE  is 3/ 4sq. units

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 9