Question

Write down the coordinates of the image of the point (2-3) under reflecting about the line joining the points (3, 5) and (3,7) ​

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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