Question 9

Step 1 · Complete Figure 1 (Top Left)

The original bent line is completed by adding two lines to form a symmetric pentagon.

• Vertices of the completed shape: $(1, 4)$, $(3, 5)$, $(6, 3)$, $(3, 1)$, and $(1, 2)$
• Line of symmetry: Horizontal line passing through $y = 3$
• Points $(1, 4)$ and $(1, 2)$ are reflections of each other across $y = 3$.
• Points $(3, 5)$ and $(3, 1)$ are reflections of each other across $y = 3$.
• Point $(6, 3)$ lies on the line of symmetry.

Step 2 · Complete Figure 2 (Top Middle)

The original L-shaped line is completed by adding two lines to form a symmetric hexagon.

• Vertices of the completed shape: $(3, 5)$, $(3, 3)$, $(5, 3)$, $(5, 1)$, $(3, 1)$, and $(3, 5)$
• Line of symmetry: Vertical line passing through $x = 4$
• Points $(3, 3)$ and $(5, 3)$ are reflections of each other across $x = 4$.
• Points $(3, 1)$ and $(5, 1)$ are reflections of each other across $x = 4$.

Step 3 · Complete Figure 3 (Top Right)

The original figure is completed by adding two lines to form a symmetric octagon.

• Vertices of the completed shape: $(1, 5)$, $(3, 4)$, $(4, 5)$, $(4, 3)$, $(6, 2)$, $(6, 4)$, $(4, 6)$, and $(3, 7)$
• The shape is completed symmetrically as shown in the diagram.

Step 4 · Complete Figure 4 (Bottom Left)

The original U-shaped figure is completed by adding two lines to form a rectangle.

• Vertices of the completed shape: $(1, 5)$, $(4, 5)$, $(4, 2)$, and $(1, 2)$
• Lines of symmetry:
  • Horizontal line passing through $y = 3.5$
  • Vertical line passing through $x = 2.5$

Step 5 · Complete Figure 5 (Bottom Middle)

The original V-shaped figure is completed by adding two lines to form a kite.

• Vertices of the completed shape: $(1, 5)$, $(3, 3)$, $(1, 1)$, and $(5, 3)$
• Line of symmetry: Horizontal line passing through $y = 3$
• Points $(1, 5)$ and $(1, 1)$ are reflections of each other across $y = 3$.
• Points $(3, 3)$ and $(5, 3)$ lie directly on the line of symmetry.

Step 6 · Complete Figure 6 (Bottom Right)

The original shape is completed by adding two lines to form a symmetric hexagon.

• Vertices of the completed shape: $(1, 5)$, $(4, 5)$, $(6, 3)$, $(4, 1)$, $(1, 1)$, and $(1, 5)$
• Line of symmetry: Horizontal line passing through $y = 3$
• Points $(1, 5)$ and $(1, 1)$ are reflections across $y = 3$.
• Points $(4, 5)$ and $(4, 1)$ are reflections across $y = 3$.
• Point $(6, 3)$ lies on the line of symmetry.