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Question

The points on the line x+y=4 which lie at a unit distance from the line 4x+3y=10, are


A

(3,1),(7,11)

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B

(3,1),(7,11)

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C

(3,1),(7,11)

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D

(1,3),(7,11)

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Solution

The correct option is A

(3,1),(7,11)


The explanation for the correct answer.

Solve for the points on the line x+y=4

Let P(h,k) lies on x+y=4

h+k=4...(i)

We know the distance of the point (x1,y1) from the line ax+by+c=0 is

d=ax1+by1+ca2+b2

1=4h+3k-1042+321=4h+3k-1054h+3k10=±54h+3k=15(ii)4h+3k=5(iii)

The distance of the pointP(h,k) from the line 4x+3y=10is 1unit.

Solving (i) and (ii), we get (h,k)=(3,1)

h+k=4...(i)

4h+3k=15...(ii)

4h+3(4-h)=15h=15-12=3

Similarly,solving (i) and (iii), we get (h,k)=(-7,11)

Hence, option(A) is the correct answer.


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