join of A(2, -3) and B(5, 6) divided by x-axis in the ratio :
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Answer:
Let a point
P
(
x
,
y
)
divide the line segment
A
B
joining the points
A
(
x
1
,
y
1
)
&
B
(
x
2
,
y
2
)
in the ratio
m
:
n
.
Here the point is on the
x
−
axis.
So,
P
(
x
,
y
)
=
(
x
,
0
)
Then, by section formula we have
x
=
n
x
1
+
m
x
2
m
+
n
&
y
=
n
y
1
+
m
y
2
m
+
n
Now,
A
(
x
1
,
y
1
)
=
(
4
,
6
)
&
B
(
x
2
,
y
2
)
=
(
1
−
7
)
Therefore,
y
=
n
y
1
+
m
y
2
m
+
n
⇒
0
=
−
7
m
+
6
n
m
+
n
⇒
m
n
=
6
7
i.e.
m
:
n
=
6
:
7
⇒
x
=
n
x
2
+
m
x
1
m
+
n
⇒
x
=
7
×
1
+
6
×
4
6
+
7
=
31
13
⇒
P
(
x
,
0
)
=
P
(
31
13
,
0
)
Step-by-step explanation:
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