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=30.
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Answers
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)
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Answer:
Image point (4,3)
Step-by-step explanation: