Question

identify the preimage of the figure, then perform the reflection according to the given rule. a ( , ) b ( , ) c ( -2 , ) reflect in the y - axis a ( 2 , ) b ( , ) c ( , -2 )

Explanation:

Step1: Find coordinates of preimage

Looking at the graph:

• Point A: From origin, left 1 unit (x=-1), up 2 units (y=2), so A(-1, 2).
• Point B: Left 5 units (x=-5), y=0, so B(-5, 0).
• Point C: Left 2 units (x=-2), y=0, so C(-2, 0).

Step2: Reflect over y - axis

Reflection over y - axis rule: \((x,y)\to(-x,y)\)

• For A(-1, 2): \(x=-(-1)=1\), so A'(1, 2).
• For B(-5, 0): \(x=-(-5)=5\), so B'(5, 0).
• For C(-2, 0): \(x=-(-2)=2\), so C'(2, 0).

Answer:

Preimage coordinates:
A(-1, 2), B(-5, 0), C(-2, 0)
Reflected coordinates:
A'(1, 2), B'(5, 0), C'(2, 0)