COORDINATE GEOMETRY
…(ii)
Q. Name the type of quadrilateral formed, if any, by the
following points, and give reasons for your Answer.
(i)
Let A (–1, –2),
B (1, 0) ,
C (–1, 2),
D (–3, 0)
∴ AB =
[1
–
(–1)
2
+
[0
2
∴ AB =
(2)
2
+
(2)
∴ AB =
4
∴ AB =
8
–
(–2)
2
]
]
+
4
∴ AB =
2
2
∴ BC =
(–1
–
1)
2
+
(2
2
–
0)
∴ BC =
(–2)
2
+
(2)
2
∴ BC =
4
∴ BC =
8
+
4
∴ BC =
2
2
∴ CD =
[–3
–
(–1)
2
+
(0
2
∴ CD =
(–2)
2
+
(–2)
∴ CD =
4
∴ CD =
8
–
2)
2
]
+
4
∴ CD =
2
2
Sol.
(–1, –2) , (1, 0) , (–1, 2) , (–3, 0)
x1 = 1,
y1 = 0,
x2 = -1,
y2 = 2
x2 = –3,
x1 = -1,
y2 = 0
y1 = 2,
Let us find AB
Let us find BC
Let us find CD
Let the coordinates of C be (x1, y1).
Let the coordinates of D be (x2, y2).
What is the formula to find distance between two points ?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
What is the formula to find distance between two points ?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
x1 = -1,
x2 = 1,
y2 = 0
y1 = –2,
A quadrilateral has four sides
So, we need to find all four sides of quadrilateral
What is the formula to find distance between two points ?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
…(i)
…(iii)
AB =
2
2
…(i)
BC =
2
2
…(ii)
AC =
2
2
…(iii)
Q. Name the type of quadrilateral formed, if any, by the
following points, and give reasons for your Answer.
∴ AD =
(–3
+
1)
2
+
(0
2
+
2)
∴ AD =
[–3
–
(–1)]
2
+
[0
2
∴ AD =
(–2)
2
+
(2)
∴ AD =
4
∴ AD =
8
–
(–2)]
2
+
4
∴ AD =
2
2
A (–1, –2),
B (1, 0) ,
C (–1, 2),
D (–3, 0)
Sol.
x2 = –3,
x1 = –1,
y2 = 0
y1 = –2
Let the coordinates of A be (x1, y1).
Let the coordinates of D be (x2, y2)
Let us find AD
What is the formula to find distance between two points ?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
…(iv)
∴
AB
=
BC
[From (i), (ii), (iii) and (iv)]
=
AC
=
AD
□ABCD is a Rhombus.
Q. Name the type of quadrilateral formed, if any, by the
following points, and give reasons for your Answer.
Diag AC =
[–1
–
(–1)]
2
+
[2
2
AC =
0
+
(4)
AC =
16
–
(–2)
2
AC =
4
]
Diag BD =
(–3
–
1)
2
+
(0
2
∴ BD =
(–4)
+
0
∴ BD =
16
–
0)
∴ BD =
4
2
In □ ABCD,
AB
=
BC
=
CD
=
AD
and
Diagonal AC
=
Diagonal BD
Hence, □ ABCD is a square
A (–1, –2),
B (1, 0) ,
C (–1, 2),
D (–3, 0)
Sol.
x2 = –1,
y2 = 2
x1 = –1,
y1 = -2
x2 = –3,
y2 = 0
x1 = 1,
y1 = 0
Let the coordinates of B be (x1, y1).
Let the coordinates of D be (x2, y2).
Let us find diag. BD
Let us find AC
∴ AC =
(–1
+
1)
2
+
(2
2
+
2)
□ABCD is a Rhombus.
∴
∴
∴
AB
=
BC
=
AC
=
AD
Let the coordinates of C be (x2, y2).
Let the coordinates of A be (x1, y1).
What is the formula to find distance between two points ?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
What is the formula to find distance between two points ?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2