The coordinate of D is (1,1).
Step-by-step explanation:
Given,
The coordinates of the square are A(1,5), B(5,5), C(5,1)
To find the the coordinate of D
Formula
We know that the diagonals of a square bisects each other.
And mid point of any two coordinates ([tex]x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] will be [tex]\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2}[/tex])
Let,
O be the mid point of diagonal AC
So, coordinates of O is [tex](\frac{1+5}{2} ,\frac{5+1}{2} )[/tex] = (3,3)
Hence, O is also the mid point of diagonal BD.
Let, coordinates of D is (x,y)
According to the formula
[tex]\frac{5+x}{2}[/tex] = 3 and [tex]\frac{y+5}{2}[/tex] = 3
or, 5+x = 6 and y+5 = 6
or, x=1 and y=1
So,
The coordinate of D is (1,1).
