Describe the single transformatthat has the same effect as reflecting across the line x = 1 followed by a reflection across the line x = 5
we want a full answer man
is that the full answer?
across x=1: (x,y) -> (1+(1-x),y) = (2-x,y)
across x=5: (x,y) -> (5+(5-x),y) = (10-x,y)
so, the combination yields (x,y) -> (10-(2-x),y) = (8+x,y)
try it with a few points to convince yourself.
To find the single transformation that has the same effect as reflecting across the line x = 1 followed by a reflection across the line x = 5, you can imagine a point on the coordinate plane and trace its path through the two reflections.
1. Start with a point P(x, y) on the coordinate plane.
2. Reflect P across the line x = 1. This means that the x-coordinate of P will become 1 - (x - 1) = 2 - x, and the y-coordinate remains unchanged. So the new point is P'(2 - x, y).
3. Now, we need to reflect P' across the line x = 5. Similar to the previous reflection, the x-coordinate of P' will become 5 - (2 - x) = 3 + x, and the y-coordinate remains unchanged. Therefore, the final reflected point is P''(3 + x, y).
Hence, the single transformation that has the same effect is a reflection across the line x = 3. This transformation will directly map point P(x, y) to P''(3 + x, y).