Question

A square 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 please im struggling

Answer 1

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

Hope this helps :)

Explanation:

Answer 2

Answer: 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

`\left((2* 10+5* a)/(2+5),(2* 1+5* b)/(2+5)\right)=(6,-3)\\\\\\\Rightarrow \left((20+5a)/(7),(2+5b)/(7)\right)=(6,-3)\\\\\\\Rightarrow (20+5a)/(7)=6,~~~~~(2+5b)/(7)=-3\\\\\\\Rightarrow 20+5a=42,~~~~\Rightarrow 2+5b=-21\\\\\\\Rightarrow 5a=22,~~~~~~~~~~\Rightarrow 5b=-23\\\\\\\Rightarrow a=4.4,~~~~~~~~~~~\Rightarrow b=-4.6.`

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,

`\textup{mid-point of DF}=\textup{mid-point of AE}\\\\\\\Rightarrow \left((c+4.4)/(2),(d-4.6)/(2)\right)=\left((2.8+6)/(2),(-3-3)/(2)\right)\\\\\\\Rightarrow \left((c+4.4)/(2),(d-4.6)/(2)\right)=\left((8.8)/(2),(-6)/(2)\right)\\\\\\\Rightarrow (c+4.4)/(2)=(8.8)/(2),~~~~~~(d-4.6)/(2)=-(6)/(2)\\\\\\\Rightarrow c+4.4=8.8,~~~~~\Rightarrow d-4.6=-6\\\\\Rightarrow c=4.4,~~~~~~~~~~~~\Rightarrow d=-1.4.`

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).