COORDINATE GEOMETRY
A (–1, 7),
B (4, –3)
= 2 : 3
=
2
(4)
+
3
(–1)
2
+
3
=
8
+
(–3)
5
=
5
5
=
2
(–3)
+
3
(7)
2
+
3
=
–6
+
21
5
=
15
5
3
∴ P (1, 3)
By using section formula, we get
x =
m1
x2
+
m2
x1
m1 + m2
y =
m1
y2
+
m2
y1
m1 + m2
=
y
Sol.
m1:m2
∴
Q. Find the coordinates of the points which divides the join of
(–1, 7) and (4, –3) in the ratio 2:3.
3
A
P
B
(–1,7)
(x, y)
(4, –3)
=
x
∴
1
Let the co-ordinates of A be (x1, y1)
Let the co-ordinates of B be (x2, y2)
We have co-ordinates of two points and the ratio
Let us substitute the values
Which formula is used to find co-ordinates of P?
,
+
m1x2
m2 x1
+
m2
m1
x
=
+
m1y2
m2y1
+
m2
m1
y
=
x1 = –1,
y1 = 7
x2 = 4,
y2 = –3
Sol.
3AB
7
∴
PB
AB
=
–
A
P
B
(–2, –2)
(x, y)
(2, –4)
AP
+
PB
=
AB
+
PB
=
AB
3AB
7
∴
PB
=
7AB
7
–
3AB
PB
=
4
7
∴
AB
∴
AP : PB
=
3 : 4
AP
=
3
7
AB
∴
A
P
B
(–2, –2)
(x, y)
(2, –4)
y =
m1
y2
+
m2
y1
m1 + m2
x =
m1
x2
+
m2
x1
m1 + m2
A (–2, –2),
B (2, –4)
= 3 : 4
=
3
(2)
+
4
(–2)
3
+
4
=
6
–
8
7
–2
7
=
3
(–4)
+
4
(–2)
3
+
4
=
–12
–
8
7
–20
7
By using section formula, we get
=
y
Sol.
m1:m2
∴
=
x
∴
Let the co-ordinates of B be (x2, y2)
Let us substitute the values
x1 = –2,
y1 = –2
x2 = 2,
y2 = –4
P =
–2
7
,
–20
7
Let the co-ordinates of A be (x1, y1)
Which formula is used to find co-ordinates of P?
,
+
m1x2
m2 x1
+
m2
m1
x
=
+
m1y2
m2y1
+
m2
m1
y
=