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Three vertices of a square have coordinates A(2, 4), B(5, –1), and C(0, –4). Give the coordinates of the fourth vertex, D, in ordered pair (x, y) form.

 Mar 22, 2022
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AB = BC = CD by the definition of square ( I didn't forget DA ). 

Thus we can use distance formula to calculate length AB, which has length sqrt(34) units, and slope -5/3. Thus CD should also have slope -5/3, and length sqrt(34) units. 

Point D should be on line y = -5x/3 - 4. DA has equation y = 3x/5 + 2.8 (perpendicular).

Thus we can solve for the x coodinate of D, which is obtained by using transitive property:

 

Point D has coordinates (-3,1)

x = -3

y = 1

 

 

u could also use desmos lol 

 Mar 22, 2022

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