Question

If the image of the point (2,1) with respect to a line mirror be (5,2),find the equation of the mirror

Answer 1

Answer:

Step-by-step explanation:

Let the equation of the mirror be, y=mx+c, where m is the slope of the points (2,1)  and (5,2).

Therefore, m=$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{2-1}{5-2}=\frac{1}{3}$.

Now, Slope of the mirror will be:

$m{\times}\frac{1}{3}=-1$

$m=-3$

The mid point of  (2,1)  and (5,2) is $(\frac{5+2}{2},\frac{2+1}{2})$

=$(\frac{7}{2},\frac{3}{2})$

Since the mid point of  (2,1)  and (5,2) lies on y=mx+c, therefore

$\frac{3}{2}=(-3){\times}\frac{7}{2}+c$

$c=12$

Hence, the equation of the line mirror is:

$y=mx+c$

$y=(-3)x+12$

$3x+y=12$