COORDINATE GEOMETRY
–
(5
0)2
=
+
–
(–3
1)2
–
(x
0)2
+
–
(6
1)2
∴
(5)
+
(–4)
=
x
+
5
∴
2
2
2
2
25
+
16
=
x
+
25
2
x
=
+
–
4
∴
=
(x
–
0)
2
+
(6
2
–
1)
QR
∴
=
x
+
5
2
2
∴
(
x2 = 16 )
=
16
+
25
QR
QR
QR
=
41
Q
P
(5, –3)
R
By distance formula,
Sol. Q (0, 1), P(5, –3) R (x, 6)
(0, 1)
QP
=
QR
QP = QR
∴
x2 = x,
y2 = 6
Squaring both side
Let the coordinates of P be (x2, y2)
Let the coordinates of Q be (x1, y1)
Let the coordinates of R be (x2, y2)
Let the coordinates of Q be (x1, y1)
EQUIDISTANT means ‘Equal Distance’.
We need to find
co-ordinates of point R.
Which is the formula to find length of QP and QR?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
Which is the formula to find length of QR?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
x2 = x,
y2 = 6
Let the coordinates of Q be (x1, y1).
Let the coordinates of R be (x2, y2).
(x ,6)
x2 = 5,
y2 = –3
x1 = 0,
y1 = 1
x1 = 0,
y1 = 1
x1 = 0,
y1 = 1
Q. If Q (0,1) is equidistant from P (5,–3) and R(x,6), find the values of x, Also find the distances QR and PR.
x2 = 16
x
=
+
–
4
Let the coordinates of P be (x1, y1)
Let the coordinates of R be (x2, y2)
x
When
=
4,
P
=
(5,
–3),
R
=
(4,
6)
∴
PR
=
(4
–
5)
2
+
[6
2
–
(–3)
=
(–1)
+
(9)
2
2
=
1
+
81
∴
PR
∴
PR
=
82
∴
PR
x
When
=
–4,
P
=
(5,
–3),
R
=
(–4,
6)
∴
PR
=
(–4
–
5)
2
+
[6
2
–
(–3)
=
(–9)
+
9
2
2
=
81
+
81
∴
PR
∴
PR
=
2
∴
PR
]
]
9
Q. If Q (0,1) is equidistant from P (5,–3) and R(x,6), find the values of x, Also find the distances QR and PR.
x1 = 5,
y1 = –3
x2 = 4,
y2 = 6
Which is the formula to find length of PR?
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
Which is the formula to find length of PR?
x1 = 5,
y1 = –3
Q
P
(5, –3)
R
(0, 1)
(x ,6)
+
–
–
(
)
(
)
x2
x1
y2
y1
2
2
Let the coordinates of R be (x2, y2)
Let the coordinates of P be (x1, y1)
y2 = 6
x2 = –4,