Question

The point A (-7,5) is reflected over the line x = -5, and then is reflected over the line x= 2. What are the coordinates of

A?
o (7, 19)
O (10,5)
(7,5)
(10, 19)

Answer 1

(7, 5) is the final reflection of the point.

Explanation:

We are given point A(-7, 5) which is first reflected over the line
`x= -5`.

The minimum distance of the point A(-7, 5) from the line
`x= -5` is 2 units across the horizontal path (No change in y coordinate).

Point A lies 2 units on the left side of the line
`x= -5`.

So, its reflection will be 2 units on the right side of
`x= -5`.

Let its reflection be A' which has coordinates as (-5+2,5) i.e. (-3, 5).

Now A'(-3, 5) is reflected on the line
`x=2`.

The minimum distance of the point A'(-3, 5) from the line
`x=2` is 5 units across the horizontal path (No change in y coordinate).

Point A' lies 5 units on the left side of the line
`x=2`.

So, its reflection will be 5 units on the right side of
`x=2`.

Let its reflection be A'' which has coordinates as (2+5, 5) i.e (7, 5) is the final reflection of the point..

Please find attached image.

(7, 5) is the final reflection of the point.