# if image of the point (2,1) with respect to a line mirror be (5,2), find the equation of the miror.....

parth pankaj tiwary
18 Points
14 years ago

Let point (2,1) be A and (5,2) be B......... First find the equation of AB..... which i hope u can easily find.

After that the slope of the so called mirror will be -3  as mirror is always perpendicular to the image.........

After that find the midpoint of AB..........For sure this point wil lie on the mirror........Now u got slope and a point.....

its easy to find the equation now....... the answer will be 6x+2y-24=0

Nehal Wani
21 Points
14 years ago

Mid Point Of (2,1) and (5,2) is (7/2,3/2)

Slope of line joining (2,1) and (5,2) : 1/3

Slope of mirror line : -3

Equation of mirror line: [y-3/2]/[x-7/2]=-3

(2y-3)/(2x-7)=-3

2y-3=21-6x

2y+6x-24=0

y+3x-8=0

Sneha vyas
21 Points
6 years ago
First we will find the midpoint of (5,2) and (1,2),
(2+5/2 , 2+1/2)
i.e ( 7/2 , 3/2 )
Now...we will find the slope of line formed by points (5,2) and (1,2)
2-1/5-2=
So slope is 1/3
We will find slope of line perpendicular to this line with thw slope 1/3....
So the slope of 2 perpendicular lines has a product of -1,
Hence the slope of the line is  m×1/3=-1 => m=-3
NOW,
find eq. Of line passing through point (5,2) and having a slope of -3
(y-3/2)/(x-7/2) =-3
2y-3/2x-7=-3
2y+6x=24
y=-3x+12