In the adjoining figure, ABCD is a square whose
vertex A is (2,0). Find the coordinates of B,C,D.
Answers
Answer:
I don't know what is the answer but I will try to get the answer
Answer:
Given ABCD is a square with vertices A(0,0),B(2,0),C(2,2),D(0,2)
It is rotated about a line in anticlockwise direction with an angle of 30
0
.
Equation of line passing through A(0,0) making an angle of 30
0
with positive direction of x−axis at a distance of r units
cos30
0
x−0
=
sin30
0
y−0
=r
⇒
3
/2
x
=
1/2
y
=r
So, the coordinates of any point lying on this line is of the form (
2
3
r
,
2
r
)
Since, point B
′
is at a distance of 2 units, new coordinates of B are (
3
,1)
AD line makes an angle of 120
0
with positive direction of x−axis
cos120
0
x−0
=
sin120
0
y−0
=r
⇒
−1//2
x
=
3
/2
y
=r
So, the coordinates of any point lying on this line is of the form (
2
−r
,
2
3
r
)
Since, point D
′
is at a distance of 2 units
So, new coordinates of D are (−1,
3
)
Slope of BD is
−1−
3
3
−1
=
3
−2
Equation of BD is
y−
3
=(
3
−2)(x+1)
⇒(2−
3
)x+y=2(
3
−1)