Question

find coordinates of the point where image of an object kept at point (2,1) is formed wirh respect to the mirror kept along the line x+y-5=0​

Answer 1

Answer:

Image point (4,3)  

Step-by-step explanation:

find coordinates of the point where image of an object kept at point (2,1) is formed with respect to the mirror kept along the line x+y-5=0​

Let say image Point = (x , y)

Line Joining point (2,1) & image Point (x , y)  Would be ⊥ to Mirror (x + y - 5) = 0

Mirror line  y = -x + 5

=> miror line Slope = -1

Slope of perpendicular line = -1/(-1) = 1

y = x + c

1 = 2 + c

=> c = -1

=> y = x - 1

intersection point of of y = x -1   &  y =-x + 5

x - 1 = -x + 5

=> 2x = 6

=> x = 3

& y = 2

Intersection point (3 , 2) will be equidistant from (2,1)  & image Point(x ,y)

(3 - 2)² + (2 - 1)²  = (x - 3)²+ (y - 2)²

putting y = x - 1

=> 1 + 1 = (x-3)² + (x -3)²

=>(x-3)² = 1

=> x - 3 = 1

=> x = 4  or  2

=> y = 3   or  1

(2 , 1) is point itself

=> Image point (4,3)