The opposite sides of a rhombus are congruent.
The missing coordinates of point D is (5,2)
How to determine the missing coordinates
The coordinates are given as:
A = (1,1)
B = (3,5)
C =(7,7)
Start by calculating the distance BC using the following distance formula
[tex]BC = \sqrt{(x_2 -x_1)^2 + (y_2-y_1)^2[/tex]
So, we have:
[tex]BC = \sqrt{(7 -3)^2 + (7-5)^2[/tex]
Next, calculate the distance AD
[tex]AD = \sqrt{(x - 1)^2 + (y - 1)^2[/tex]
The side lengths are equal. So, we have:
[tex]\sqrt{(x - 1)^2 + (y - 1)^2} = \sqrt{(7 -3)^2 + (7-5)^2}[/tex]
Cancel the square roots
[tex](x - 1)^2 + (y - 1)^2 = (7 -3)^2 + (7-5)^2[/tex]
[tex](x - 1)^2 + (y - 1)^2 = 4^2 + 2^2[/tex]
By comparison, we have:
[tex]x -1 = 4[/tex]
[tex]y -1 = 2[/tex]
Solve for x and y
[tex]x = 5[/tex]
[tex]y = 2[/tex]
Hence, the missing coordinates of point D is (5,2)
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