Question

What are the coordinates of A after reflecting across the line x = 3? (2, 3)

(3, 2) (3, 4) (3, -2)​

Answer 1

Here we can not see point A, so i will answer in a general way.

Let's suppose that point A is (a, b)

Now, if we do a reflection over a given line, the (perpendicular) distance between our original point to the line is the same as the distance between the reflected point and the line.

So for example if we have the point (x, y) and we do a reflection over the line x = k.

The distance between our point and the line is:

x - k

So the new point must be also at a distance of (x - k) from line x = k.

The only other point that meets this condition is (k - (x - k), y) = (2k - x, y)

Now remember that point A is (a, b)

And we do a reflection over x = 3

The distance between our point and the line is:

D = I(a - 3)I

Then the reflection will be:

(3 - (a - 3), b) = (6 - a, b)

Where (a, b) where the original coordinates of point A.