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National and Regional Contests
Spain Contests
Spain Mathematical Olympiad
1983 Spain Mathematical Olympiad
5
5
Part of
1983 Spain Mathematical Olympiad
Problems
(1)
coordinates of vertices of square wanted
Source: Spanish Mathematical Olympiad 1983 P5
12/23/2022
Find the coordinates of the vertices of a square
A
B
C
D
ABCD
A
BC
D
, knowing that
A
A
A
is on the line
y
−
2
x
−
6
=
0
y -2x -6 = 0
y
−
2
x
−
6
=
0
,
C
C
C
at
x
=
0
x = 0
x
=
0
and
B
B
B
is the point
(
a
,
0
)
(a, 0)
(
a
,
0
)
, being
a
=
log
2
/
3
(
16
/
81
)
a = \log_{2/3}(16/81)
a
=
lo
g
2/3
(
16/81
)
.
analytic geometry
square