Question

If A(4,0) and C(0,-4) are the coordinates of the diagonal of a square ABCD, find the area of a square.

Answer 1

Answer:

Plot the points, A, C and D. Join them using straight lines to complete the square.

Hence B =(4,4).

Draw diagonals AC and BD.

The point of intersection of the diagonals of a square is the mid pt of the any diagonal.

The co-ordinates of the mid-pt of a segment joining AB and CD are ((a+c)/2,(b+d)/2).

Hence, point of intersection of diagonals =(1,7)

solution

Answer 2

Answer:

16 unit²

Step-by-step explanation:

Given, A(4,0) ; C(0,-4) as coordinates of diagonal of square

By distance formula ;

AC=√{(4-0)²+(0+4)²

AC=√(4)²+(4)²

AC=√16+16

AC=√32

AC=4√2 units

Now,

Area of square= 1/2*d² (diagonal AC)

= 1/2*(4√2)²

= 16 unit²