The pointegral on the line x + y = 4 which lie at a unit dis... | MATH - DISTANCE BETWEEN TWO LINES, PERPENDICULAR | SolveeIt | Solveeit

Today, August 18

Question

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

A

(3, 1), (– 7, 11)

B

(3, 1), (7, 11)

C

(– 3, 1), (– 7, 11)

D

(1, 3),(– 7, 11)

Answer

(3, 1), (– 7, 11)

Explanation

Solution

Let the point be (x₁, y₁)

then x₁ + y₁ = 4 ….(i)

&

Ž $\frac { 4 x _ { 1 } + 3 y _ { 1 } - 10 } { 5 }$ = ± 1

Taking positive sign

Ž $4 x _ { 1 } + 3 y _ { 1 } = 15$ …… (ii)

Taking negative sign

solve (i) & (ii) Ž point is (3, 1)

& solve (i) & (iii) Ž point is (– 7, 11)