If A(4,0) and C(0,-4) are the coordinates of the diagonal of a square ABCD, find the area of a square.
Answers
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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
Answered by
1
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
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