Answer:
11) (x, y) ⇒ (-4-x, y)
12) (x, y) ⇒ (-x, y)
13) (x, y) ⇒ (-4-x, y)
14) (x, y) ⇒ (4-x, y)
Step-by-step explanation:
In general if M is the midpoint of a point (A) and its reflection (A'), then we have ...
(A +A')/2 = M
A + A' = 2M . . . . . . multiply by 2
A' = 2M -A . . . . . . . subtract A
When a point is reflected across the vertical line x = p, all of the y-coordinate values remain unchanged. So, for A=(x, y) and M=(p, y), we have ...
A' = 2(p, y) -(x, y) = (2p-x, 2y-y)
A' = (2p -x, y)
So, the reflection transformation across the line x = p is ...
(x, y) ⇒ (2p-x, y)
__
The questions on this page all involve reflection across various vertical lines (x = p), so the transformations will all look like the one above, but with different constants.
The line of reflection is the perpendicular bisector of the segment between the point and its image. If the point and image are the same point, that point is on the line of reflection (see 13 and 14).
11) p = -2, so the transformation rule is ...
(x, y) ⇒ (-4-x, y)
__
12) p = 0, so the transformation rule is ...
(x, y) ⇒ (-x, y)
__
13) Same as 11. The transformation rule is ...
(x, y) ⇒ (-4-x, y)
__
14) p = 2, so the transformation rule is ...
(x, y) ⇒ (4-x, y)
_____
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