Question

if A(6,1), B(8,2) and C(9,4) are three vertices of a parallelogamABCD.Find the fourth vertex
IfE is the mid-pont of Dc, then find the area ofA ADe.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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 (x1,y1) = A (6,1),

E(x2,y2) = E(8,7/2) and D (x3,y3) = D(7,3)

Now  Area (ΔABC) = 1/2[x1(y2 - y3)+x2(y3 - y1) + x3(y1 - y2)]

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

=1/2[3/2]

=3/4 sq. unit .