totally stuck can someone help please
P P'(–8, –3) for the glide reflection where the translation is (x, y) (x –2, y –5) and the line of reflection is y = –x. Find the coordinates of P.
So, are you giving P' as the result of the transformation, and want to know P, the original point?
To find the coordinates of point P after the glide reflection, we need to apply both the translation and the reflection to the given point P'(–8, –3).
Step 1: Translation.
The translation (x, y) (x – 2, y – 5) means that we need to move every point 2 units to the right and 5 units down. To apply this translation to P', we need to add the translation values to the coordinates of P'.
P'(–8, –3) + (–2, –5) = (–8 + (–2), –3 + (–5)) = (–10, –8)
So, after the translation, P' becomes P''(–10, –8).
Step 2: Reflection.
The line of reflection is y = –x. To reflect a point over this line, we need to find the image of the point by swapping the x and y coordinates and changing the sign of one of them.
Applying the reflection, we have P''(–10, –8) -> P'''(8, 10).
Therefore, the coordinates of P after the glide reflection are (8, 10).