COORDINATE GEOMETRY
A
B
C
(7, –3)
(5, 3)
(3, –1)
Q. Find the lengths of the medians of Δ ABC whose vertices are
A (7, -3), B (5, 3) and C (3, –1).
Q
R
Sol.
Let AP, BQ and CR be the medians of
sides BC, CA and AB resp.
P is midpoint of seg BC
By midpoint formula,
P
=
=
∴
8
2
,
2
2
5
+
3
2
,
3
–
1
2
(4, 1)
=
P
P
=
x1
+
x2
2
,
y1
+
y2
2
Let us substitute the values.
What is a median?
A line segment joining the vertex of a triangle to the midpoint of its opposite side.
Since, we have co-ordinates of A and P. So, let us apply distance formula to find the length of AP.
P
P
x1 = 5,
y1 = 3
x2 = 3,
y2 = –1
Which formula is used to find the length of AP ?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
We need to find the lengths of AP, BQ and CR.
For using distance formula, we require the co-ordinates of A and P.
?
Which formula is used to find
co-ordinates of P?
Mid-Point Formula
,
+
x1
x2
2
+
y1
y2
2
Let the co-ordinates of B be (x1, y1)
Let the co-ordinates of C be (x2, y2)
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
AP
=
+
–
[
]2
4
7
=
+
–
(4
7)2
=
+
(–3)2
=
(4)2
9
=
+
16
25
=
AP
∴
=
–
[
]2
1
(–3)
+
(1
3)2
5 units
Q. Find the lengths of the medians of Δ ABC whose vertices are
A (7, -3), B (5, 3) and C (3, –1).
Sol.
A
(7, –3)
P
(4, 1)
By distance formula,
A
B
C
(7, -3)
(5, 3)
(3, -1)
Q
R
P
x1 = 7,
y1 = –3
x2 = 4,
y2 = 1
Let the co-ordinates of A be (x1, y1)
Let the co-ordinates of P be (x2, y2)
Which formula is used to find length of AP?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2