write the coordinates of the vertices after a reflection over the line $x = 1$.
write the coordinates of the vertices after a reflection over the line $x = 1$.
Answer
Explanation:
Step1: Recall the reflection formula
For a reflection over the line (x = a), the formula for the (x)-coordinate of a point ((x,y)) is (x'=2a - x), and the (y)-coordinate remains the same ((y'=y)). Here (a = 1).
Step2: Find the new (x)-coordinate for each point
- For point (K(3,-1)): (x'=2\times1 - 3=2 - 3=-1), (y'=-1). So the new coordinate is ((-1,-1))
- For point (N(3,6)): (x'=2\times1 - 3=2 - 3=-1), (y' = 6). So the new coordinate is ((-1,6))
- For point (M(8,6)): (x'=2\times1 - 8=2 - 8=-6), (y' = 6). So the new coordinate is ((-6,6))
- For point (L(8,-1)): (x'=2\times1 - 8=2 - 8=-6), (y'=-1). So the new coordinate is ((-6,-1))
Answer:
(K'(-1,-1)), (N'(-1,6)), (M'(-6,6)), (L'(-6,-1))