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) ​

Answer 1

(4 , -3)

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.