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Sweden Contests
Swedish Mathematical Competition
1975 Swedish Mathematical Competition
1
1
Part of
1975 Swedish Mathematical Competition
Problems
(1)
AQ_|_QP , A(1,0), L lies on line y = kx
Source: 1975 Swedish Mathematical Competition p1
3/26/2021
A
A
A
is the point
(
1
,
0
)
(1,0)
(
1
,
0
)
,
L
L
L
is the line
y
=
k
x
y = kx
y
=
k
x
(where
k
>
0
k > 0
k
>
0
). For which points
P
(
t
,
0
)
P(t,0)
P
(
t
,
0
)
can we find a point
Q
Q
Q
on
L
L
L
such that
A
Q
AQ
A
Q
and
Q
P
QP
QP
are perpendicular?
analytic geometry
algebra