Question

The point P(1,1) is translated parallel to 2x=y in the first quadrant through a unit distance.The coordinates of nee position of P is

Answer 1

Dear Student,
Please find below the solution to the asked query:

Given,y=2x
Given a point p(1,1)
let line L=y=mx+c
y=2x+c(1,1) lies on this line
1=2+c
c=−1
hence,y=2x−1
let new point be (h,k)
it will lie on L
k=2h−1

√(h−1)^2+(k−1)^2=1

(h−1)^2+(k−1)^2=1
(h−1)^2+(2h−2)^2=1

h^2+1−2h+4h^2+4−8h=15

h^2−10h+4=0

h=(10±√[100−4×4×5]) ÷ (2×5)
=[10±√20] ÷ 10

=1±[2√5 ÷ 10]

=1±[1÷√5]

k=2h−1
=2± [[2÷√5】−1]

=1± [2÷√5]

hence (h,k)= (1±[1÷√5] ,1±[2÷√5])

correct ans is 2

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