COORDINATE GEOMETRY
and Midpoint Formula
y =
m1
y2
+
m2
y1
m1 + m2
P (4, –1),
Q (–2, –3)
= 1 : 2
=
1
(–2)
+
2
(4)
1
+
2
=
–2
+
8
3
=
6
3
=
1
(–3)
+
2
(–1)
1
+
2
=
–3
–
2
3
–5
3
By using section formula, we get
=
y
Sol.
, m1:m2
∴
=
x
∴
2
Let the co-ordinates of Q be (x2, y2)
Let the co-ordinates of P be (x1, y1)
Let us substitute the values
P
R
S
(4, –1)
Q
(–2, –3)
Let the points R and S be the points
of trisection of seg PQ.
∴
R =
2
–5
3
,
( )
Now, point R divides seg PQ in the ratio 1 : 2
x =
m1
x2
+
m2
x1
m1 + m2
2
1
2
:
Q. Find the coordinates of the points of trisection of the line
segment joining (4, –1) and (–2, –3).
i.e a line segment divided in three equal parts
x1 = 4
y1 = –1
x2 = –2,
y2 = –3
Which formula is used to find co-ordinates of R?
,
+
m1x2
m2 x1
+
m2
m1
x
=
+
m1y2
m2y1
+
m2
m1
y
=
2
–5
3
,
( )
We have co-ordinates of two points and the ratio
S
=
2
–
2
2
,
–
3
2
Now, point S is the midpoint of seg RQ
By Midpoint Formula
∴
Q. Find the coordinates of the points of trisection of the line
segment joining (4, –1) and (–2, –3).
R
, Q (–2, –3)
x1 = 2,
x2 = –2,
y2 = –3
Sol.
P
R
S
(4, –1)
Q
(–2, –3)
2
–5
3
,
( )
2
–5
3
,
( )
–5
3
y1 =
–5
3
=
0
2
,
–
9
6
–5
=
0
,
–14
6
=
0
,
–7
3
∴
S
Mid-Point Formula
,
+
x1
x2
2
+
y1
y2
2
Let the co-ordinates of Q be (x2, y2)
Let the co-ordinates of R be (x1, y1)
Which formula is used to find co-ordinates of midpoint of a segment