COORDINATE GEOMETRY
.
Sol.
P, Q and R are the mid–point of AB , BC and AC
∴
By midpoint formula ,
Coordinate of P
=
0
+
2
2
,
–1
+
1
2
=
(1 , 0)
Coordinate of Q
=
2
+
0
2
,
1
+
3
2
=
(1 , 2)
Coordinate of R
=
0
+
0
2
,
3
–
1
2
=
(0 , 1)
A
B
C
P
R
Q
(0, –1)
(2, 1)
(0, 3)
x2 = 2,
y2 = 1
x2 = 0,
y2 = 3
x1 = 2,
y1 = 1
x1 = 0,
y1 = 3
Let the co-ordinates of B be (x2, y2)
Let the co-ordinates of A be (x1, y1)
Let the co-ordinates of C be (x2, y2)
Let the co-ordinates of B be (x1, y1)
Let the co-ordinates of A be (x2, y2)
Let the co-ordinates of C be (x1, y1)
(1 , 0)
(1 , 2)
(0 , 1)
Q. Find the area of the triangle formed by joining the
mid–points of the sides of the triangle whose vertices are (0, –1),
(2, 1) and (0, 3).
Find the ratio of this area to the area of the given triangle.
Which formula is used to find co-ordinates of midpoint of a segment
Mid-Point Formula
,
+
x1
x2
2
+
y1
y2
2
x1 = 0,
y1 = –1
x2 = 0,
y2 = –1
Sol.
Q. Find the area of the triangle formed by joining the
mid–points of the sides of the triangle whose vertices are (0, –1),
(2, 1) and (0, 3).
Find the ratio of this area to the area of the given triangle.
∴
ar (ΔPQR)
=
[
1
1
2
(2
–
1)
+
1
(1
–
0)
+
0
(0
–
2)]
x1 = 1,
y1 = 0
x2 = 1,
y2 = 2
Let the co-ordinates of Q be (x2, y2)
Let the co-ordinates of R be (x3, y3)
Let the co-ordinates of P be (x1, y1)
Consider ΔPQR
Now P(1, 0),
Q(1, 2),
R(0, 1)
A
B
C
P
R
Q
(0, –1)
(2, 1)
(0, 3)
(1 , 0)
(1 , 2)
(0 , 1)
x3 = 0,
y3 = 1
=
1
2
(1
+
1
+
0)
=
1
2
×
2
∴
ar (ΔPQR)
=
1 sq.unit
Which formula is used to find area of triangle?
[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)]
1
2
Sol.
Q. Find the area of the triangle formed by joining the
mid–points of the sides of the triangle whose vertices are (0, –1),
(2, 1) and (0, 3).
Find the ratio of this area to the area of the given triangle.
∴
ar (ΔABC)
=
[
0
1
2
(1
–
3)
+
2
(3
+
1)
+
0
(–1
–
1)]
x2 = 2,
y2 = 1
A
B
C
P
R
Q
(0, –1)
(2, 1)
(0, 3)
(1 , 0)
(1 , 2)
(0 , 1)
x3 = 0,
y3 = 3
=
1
2
(0
+
8
+
0)
=
1
2
×
8
∴
ar (ΔABC)
=
4 sq.units
area (ΔPQR)
area (ΔABC)
=
1
4
or
1 : 4
ar (ΔPQR)
=
1 sq.unit
4
Which formula is used to find area of triangle?
[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)]
1
2
x1 = 0,
y1 = –1
i.e ar(ΔPQR)
Let the co-ordinates of B be (x2, y2)
Let the co-ordinates of C be (x3, y3)
Let the co-ordinates of A be (x1, y1)
Consider ΔABC
i.e ar(ΔABC)