On the portion of the straight line x + 2y = 24 intercepted between the axis is a square is constructed on the side of a line away from the origin then the point of intersection of its diagonal has the co-ordinate
Answers
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Given equation of line :
x
+
2
y
=
4
,
when
x
=
0
,
y
=
2
,
⇒
A
(
0
,
2
)
−
−
−
−
y
−
intercept.
when
y
=
0
,
x
=
4
,
⇒
B
(
4
,
0
)
−
−
−
−
x
−
intercept.
B
is
4
units right and
2
units down from
A
.
length of
A
B
=
√
2
2
+
4
2
=
√
20
=
2
√
5
,
Let
A
B
C
D
be the square, as shown in the figure.
As
A
D
is perpendicular to
A
B
, and
A
D
=
A
B
=
2
√
5
,
⇒
D
is
2
units right and
4
units up from
A
,
⇒
D
(
x
d
,
y
d
)
=
(
0
+
2
,
2
+
4
)
=
(
2
,
6
)
Similarly,
C
is
2
units right and
4
units up from
B
,
⇒
C
(
x
c
,
y
c
)
=
(
4
+
2
,
0
+
4
)
=
(
6
,
4
)
let
M
be the point of intersection of the diagonals
A
C
and
B
D
,
recall that the two diagonals of a square bisect each other,
⇒
M
is the mid-point of
A
C
or
B
D
⇒
M
(
x
m
,
y
m
)
=
(
0
+
6
2
,
2
+
4
2
)
=
(
3
,
3
)