In the coordinate plane, the point X (4, -3) is translated to the point X' (-1, 1). Under the same translation, the points Y (1, -1) and Z (6, 1) are translated to Y' and Z' , respectively. What are the coordinates of Y' and Z' ?
Answers
Answer:
Step-by-step explanation:
The correct option is C
(
1
±
1
√
5
,
1
±
2
√
5
)
Given equation of line is
y
=
2
x
.
Let the new position of point
P
be
P
′
(
x
1
,
y
1
)
Equation of line passing through
P
(
1
,
1
)
and parallel to
y
=
2
x
is
y
−
1
=
2
(
x
−
1
)
⇒
y
=
2
x
−
1
Since,
P
′
(
x
1
,
y
1
)
lies on this line
⇒
y
1
=
2
x
1
−
1
...(1)
Also, given
P
is translated to
P
′
by a unit distance
P
P
′
=
1
⇒
(
x
1
−
1
)
2
+
(
y
1
−
1
)
2
=
1
⇒
(
x
1
−
1
)
2
+
(
2
x
1
−
2
)
2
=
1
(by (1))
⇒
5
x
2
1
−
10
x
1
+
4
=
0
⇒
x
1
=
10
±
√
20
10
⇒
x
1
=
5
±
√
5
5
⇒
x
1
=
1
±
1
√
5
Put this value in (1), we get
y
1
=
2
(
1
±
1
√
5
)
−
1
⇒
y
1
=
1
±
2
√
5
Hence, the new position of
P
is
(
1
±
1
√
5
,
1
±
2
√
5
)