8. P -> P' (2, 6) for the glide reflection where the translation is (x,y) -> (x + 2, y - 2) and the line of reflection is y = - x. Find the coordinates of P.
A. (11, -3)
B. (4, 0)
C. (-11, 3)
D. (-4, 0)
I think it is B. But I'm not sure, could I get some help.
Nope, it is B 100%
yea B is correct, got it wrong with D
To find the coordinates of point P after the glide reflection, we need to apply both the translation and the reflection.
Let's start with the translation:
Given the translation (x, y) -> (x + 2, y - 2), we need to add 2 to the x-coordinate and subtract 2 from the y-coordinate.
The original coordinates of P are (2, 6). Applying the translation, we get:
(2 + 2, 6 - 2) = (4, 4)
Now, let's consider the line of reflection y = -x.
We need to reflect the translated coordinates (4, 4) across this line.
To do this, we find the equation of the line perpendicular to y = -x that passes through the point (4, 4). We can determine the slope of the perpendicular line by taking the negative reciprocal of the slope of y = -x, which is 1.
The equation of the perpendicular line passing through (4, 4) is y = 1x + b. We can substitute the coordinates to find the value of b:
4 = 1(4) + b
4 = 4 + b
b = 0
So, the perpendicular line is y = x.
To reflect a point across a line, we mirror the coordinates across the line. So for the point (4, 4), the reflection will be (-4, -4).
Therefore, the final coordinates of P after the glide reflection are given by (-4, -4).
Comparing this with the answer choices, option D (-4, 0) is the correct answer.
If P = (x,y), then we have the two transformations
(x,y) -> (x+2,y-2) -> (2-y,-(x+2))
so,
2-y = 2; y=0
-(x+2) = 6; x = -8
Hmmm. no luck.
If we reflect first, then we have
(x,y) -> (-y,-x) -> (-y+2,-x-2)
so,
-y+2 = 2; y=0
-x-2 = 6; x = -4
Looks like D to me.
You have to specify the order of operation.