Answer with explanation:
Coordinates of Point A = (2,5)
It is given that , point A and A' have symmetry with respect to the line y = 3.
→It means that , perpendicular distance of point A from line , y=3 is same as Perpendicular distance of point A' from line , y=3.
→Perpendicular distance of Point A (2,5),from, line ,y=3 is,that is from , point (2,3) is , as x coordinates are same , so
Perpendicular Distance = 5 -3 = 2 unit
X coordinate of Point A'= 2
→Distance from , Point A'(2,k) to line , y=3 that is from , point (2,3) is will be
= 2 unit
→| k -3|=2
k -3 = 2 ∧ 3 -k=2
k=2 +3 ∧ -k=2 -3
k=5 ∧ - k = -1
→k=5 ∧ k=1
So, (2,5) is coordinate of point A and (2,1) is coordinate of point A'.
The Second way is
→Mid point of A(2,5) and A'(x,y) will lie on line, y=3 that is mid point being equal to , (2,3),as drawing perpendicular from point A on line,y=3,gives point (2,3).
[tex]\frac{2 +x}{2}=2\\\\x+2=4\\\\x=4-2\\\\x=2\\\\ \frac{y+5}{2}=3\\\\y+5=6\\\\y=6-5\\\\y=1[/tex]
Coordinates of Point A'= (2,1)
