Two opposite vertices of a square are (3,4) and (−2,−1). Find the coordinates of other two vertices.
Assume A(−2,−1) and C(3,4) are two opposite vertices of a square
AC=(3−(−2),4−(−1))
∣AC∣=52+52=52 The side of the square is 5.
slopeAC=3−(−2)4−(−1)=1 Then
slopeBD=−1The equation of the BD is y=−x+b.
The center of the square is O(23−2,24−1).
Substitute
23=−21+b=>b=2
BD:y=−x+2
The angle between AB and BD is 45°. Then the equation of AB is x=−2.
y=−(−2)+2=4 B(−2,4)
The angle between CD and BD is 45°. Then the equation of CD is x=3.
y=−3+2=−1 D(3,−1)
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