A ray of light passing through the point A (1,2) is reflected at a point B on the x-axis line mirror and then passes through (5,3). Then the equation of A B is -

Question

A ray of light passing through the point A (1,2) is reflected at a point B on the x-axis line mirror and then passes through (5,3). Then the equation of A B is - (A) 5 x+4 y=13 (B) 5 x-4 y=-3 (C) 4 x+5 y=14 (D) 4 x-5 y=-6

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/3d8a8b94e89f8eaa583e36ffa5793e86-.png" /> Image of (5,3) in x-axis is (5,-3) Now, line A B will also pass through (5,-3) ∴ equation of A B is y-2=(-5/4)(x-1) 5 x+4 y=13

Q. A ray of light passing through the point $A (1, 2)$ is reflected at a point $B$ on the $x$ -axis line mirror and then passes through $(5, 3)$ . Then the equation of $A B$ is -

$5 x + 4 y = 13$

$5 x - 4 y = - 3$

$4 x + 5 y = 14$

$4 x - 5 y = - 6$

Image of $(5, 3)$ in $x$ -axis is $(5, - 3)$
Now, line $A B$ will also pass through $(5, - 3)$
$∴$ equation of $A B$ is $y - 2 = \frac{- 5}{4} (x - 1)$ $5 x + 4 y = 13$

Q. A ray of light passing through the point A(1,2) is reflected at a point B on the x-axis line mirror and then passes through (5,3). Then the equation of AB is -

5x+4y=13

5x−4y=−3

4x+5y=14

4x−5y=−6