write the coordinates of the vertices after a reflection over the y-axis.
write the coordinates of the vertices after a reflection over the y-axis.
Answer
Explanation:
Step1: Identify original coordinates
First, find the original coordinates of each vertex.
- Point ( C ): From the graph, ( x = -10 ), ( y = -2 ), so ( C(-10, -2) ).
- Point ( D ): ( x = 0 ), ( y = -2 ), so ( D(0, -2) ).
- Point ( E ): ( x = 0 ), ( y = 8 ), so ( E(0, 8) ).
- Point ( F ): ( x = -10 ), ( y = 8 ), so ( F(-10, 8) ).
Step2: Apply reflection over y - axis rule
The rule for reflecting a point ( (x, y) ) over the ( y )-axis is ( (x, y) \to (-x, y) ).
- For ( C(-10, -2) ): Apply the rule, ( x ) - coordinate becomes ( -(-10)=10 ), ( y ) - coordinate remains ( -2 ). So ( C' (10, -2) ).
- For ( D(0, -2) ): Apply the rule, ( x ) - coordinate becomes ( -0 = 0 ), ( y ) - coordinate remains ( -2 ). So ( D' (0, -2) ).
- For ( E(0, 8) ): Apply the rule, ( x ) - coordinate becomes ( -0=0 ), ( y ) - coordinate remains ( 8 ). So ( E' (0, 8) ).
- For ( F(-10, 8) ): Apply the rule, ( x ) - coordinate becomes ( -(-10) = 10 ), ( y ) - coordinate remains ( 8 ). So ( F' (10, 8) ).
Answer:
The coordinates of the vertices after reflection over the ( y )-axis are ( C'(10, -2) ), ( D'(0, -2) ), ( E'(0, 8) ), ( F'(10, 8) ).