Asquare is constructed on side ad of quadrilateral abcd such that fa lies on ab, as shown in the figure.

if ad : ab = 2 : 5, the coordinates of point f are point e has the coordinates (2.8, -3), and the coordinates of point d are

f options- (4.4,-4.6) , (4.4,-3.6) , (4.6,-4.6) , (4.6,-3.6)

d options- (4.4,-2.4) , (4.4,-1.4) , (4.6,-2.4) , (4.6,-1.4)

bruh im struggling

 The co-ordinates of F are (4.4, -4.6) and the co-ordinates of D are (4.4, -1.4).

Step-by-step explanation:  Given that a square is constructed on side AD of quadrilateral ABCD such that FA lies on AB as shown in the figure. The co-ordinates of A are (6, -3) and the co-ordinates of B are (10, 1).

Also, AD : AB = 2 : 5 and the co-ordinates of the point E are (2.8, -3).

We are to select the correct co-ordinates of the points F and D.

Let, (a, b) are the co-ordinates of F and (c, d) are the co-ordinates of D.

Since ADEF is a square, so we have

AD = DE = EF = FA.

Given that

AD : AB = 2 : 5, so  FA : AB = 2 : 5.

That is, \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{2.8+6}{2},\dfrac{-3-3}{2}\right)

We have, after applying the internal division formula that

So, the co-ordinates of F are (4.4, -4.6).

Now, since ADEF is a square, and the diagonals of a square bisect each other.

So, the mid-points of both the diagonals are same.

That is,

So, the co-ordinates of D are (4.4, -1.4).

Thus, the co-ordinates of F are (4.4, -4.6) and the co-ordinates of D are (4.4, -1.4).

F is (4.4, -4.6) and D is (4.4, -1.4).

Hope this helps :)

Step-by-step explanation: