Question

The point (−7, 4) is reflected over the line x = −3. Then,the resulting point is reflected over the line y = x.  Whereis the point located after both reflections?

Answer 1

Take into account that a reflection over the line x=-3 results in a new point wich has the same distance to the line x=-3 as the original point.

the horizontal distance between (-7,4) and linex=-3 is:

-3-(-7) = -3+7 = 4

then, the new point is 4 units to the right of line x=-3. Then, the x cooridinate of the new point si:

-3 + 4 = 1

and the points is:

(1 , 4)

the y coordinate remains the same because the reflection is over a vertical line.

Nex, a reflection over the line y = x demands the following transformation:

(x , y) => (y , x)

Then, you obtain:

(1 , 4) => (4 , 1)

The point is located at (4,1) after both reflections.