Question 9

We need to draw lines to complete each figure into a shape that has a line of symmetry.

Step 1 — Figure 1 (Top Left)

The original figure is a bent line. We add lines to complete it into a symmetric shape. The completed shape is a pentagon.

The points of the completed shape are (1,4), (3,5), (6,3), (3,1), and (1,2). This shape has a horizontal line of symmetry. This line passes 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 — Figure 2 (Top Middle)

The original figure is a 'L' shape. We add lines to complete it into a symmetric shape. The completed shape is a hexagon.

The points of the completed shape are (3,5), (3,3), (5,3), (5,1), (3,1), and (3,5). This shape has a vertical line of symmetry. This line passes through $x=4$. Points (3,5) and (5,5) are reflections of each other across $x=4$. (Note: (5,5) is not a vertex, but (3,5) is symmetric to where (5,5) would be). 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 — Figure 3 (Top Right)

The original figure is a complex bent line. We add lines to complete it into a symmetric shape. The completed shape is an octagon.

The points of the completed shape are (1,5), (3,4), (4,5), (4,3), (6,2), (6,4), (4,6), and (3,7). This shape is completed as shown in the diagram. It is intended to be a symmetric figure.

Step 4 — Figure 4 (Bottom Left)

The original figure is a 'U' shape. We add lines to complete it into a symmetric shape. The completed shape is a rectangle.

The points of the completed shape are (1,5), (4,5), (4,2), and (1,2). This shape has two lines of symmetry. One line is horizontal, passing through $y=3.5$. The other line is vertical, passing through $x=2.5$.

Step 5 — Figure 5 (Bottom Middle)

The original figure is a 'V' shape. We add lines to complete it into a symmetric shape. The completed shape is a kite.

The points of the completed shape are (1,5), (3,3), (1,1), and (5,3). This shape has a horizontal line of symmetry. This line passes through $y=3$. Points (1,5) and (1,1) are reflections of each other across $y=3$. Points (3,3) and (5,3) lie on the line of symmetry.

Step 6 — Figure 6 (Bottom Right)

The original figure is a 'Z' like shape. We add lines to complete it into a symmetric shape. The completed shape is a hexagon.

The points of the completed shape are (1,5), (4,5), (6,3), (4,1), (1,1), and (1,5). This shape has a horizontal line of symmetry. This line passes through $y=3$. Points (1,5) and (1,1) are reflections of each other across $y=3$. Points (4,5) and (4,1) are reflections of each other across $y=3$. Point (6,3) lies on the line of symmetry.