Answers

1. Answer:

   (4 , -3)

   Step-by-step explanation:

   the points (3 , 5) and (3 , 7) ​have the same x-coordinates 3

   then ,the line D joining them has the equation  

   D : x = 3

   the image of the point A(2 , -3) under reflecting about The line D ,

   lie on the line ∆ perpendicular to D and passes through A.

   ∆ perpendicular to D then the equation of ∆ is :

   ∆ : y = a   ,where a is a real number.

   Calculating ‘a’ :

   ∆ passes through A

   Then

   -3 = a

   Therefore

   the final equation of ∆ is :

   ∆ : y = -3

   Obviously, the lines D and ∆ intersect at the point M(3 , -3)

   FINAL STEP :

   Calculating the coordinates of the point B(x , y) image of the point A(2 , -3)

   M is the midpoint of the line segment AB :

   Then

   3 = (2 + x)/2 and -3 = (-3 + y)/2

   Then

   x = 4 and y = -3.

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