Question

Question No. 7
The co-ordinates of the point of reflection of the origin (0,0) in the line 4x-2y - 5 = 0 is

(1,-2)

(2,-1)

(4\5 ,-2/5)

(2,5)

Answer 1

Answer:

Let the image of the point O(0,0) is

p(h,k)

4x−2y−5=0−(i)

Equation of OP is

y−0=

2

−1

(x−0)

⇒x=−2y−(ii)

Using (ii) in (i)

4(−2y)−2y−5=0

⇒−10y=5

⇒y=

2

−1

∴x=−2(

2

−1

)=1

Hence, Q(1,

2

−1

)

∴

2

λ+0

=1,

2

k+0

=

2

−1

∴λ=0,k=−1

Hence, Image is (2,−1

Answer 2

Answer:

Let the image of the point O(0,0) is

p(h,k)

4x−2y−5=0−(i)

Equation of OP is

y−0= -1/2(x−0)

⇒x=−2y−(ii)

Using (ii) in (i)

4(−2y)−2y−5=0

⇒−10y=5

⇒y=-1/2

∴x=−2(-1/2)=1

Hence, Q(1,-1/2)

∴λ+0/2=1,

also, k+0/2=-1/2

∴λ=0,k=−1

Hence, Image is (2,−1)