Question

1. (02.01 mc)

what set of reflections would carry hexagon abcdef onto itself? (1 point)
options:

• ( x )-axis, ( y = x ), ( x )-axis, ( y = x )
• ( y = x ), ( x )-axis, ( y = x ), ( y )-axis
• ( y )-axis, ( x )-axis, ( y )-axis
• ( x )-axis, ( y )-axis, ( y )-axis

Explanation:

Step1: Identify hexagon vertices

Vertices (approx): $A(-1,1), B(-3,1), C(-4,2), D(-3,3), E(-1,3), F(0,2)$

Step2: Test Option 2 (y=x, x-axis, y=x, y-axis)

Substep2a: Reflect over $y=x$

Rule: $(x,y)\to(y,x)$
New points: $(1,-1), (1,-3), (2,-4), (3,-3), (3,-1), (2,0)$

Substep2b: Reflect over x-axis

Rule: $(x,y)\to(x,-y)$
New points: $(1,1), (1,3), (2,4), (3,3), (3,1), (2,0)$

Substep2c: Reflect over $y=x$

Rule: $(x,y)\to(y,x)$
New points: $(1,1), (3,1), (4,2), (3,3), (1,3), (0,2)$

Substep2d: Reflect over y-axis

Rule: $(x,y)\to(-x,y)$
New points: $(-1,1), (-3,1), (-4,2), (-3,3), (-1,3), (0,2)$
These match original vertices.

Answer:

B. y = x, x-axis, y = x, y-axis