Question

refer to the figure at the right.

1. draw the line(s) of symmetry in the figure.
2. locate the center of symmetry for the figure.
3. what is the order and magnitude of symmetry for the figure?

Explanation:

Question 15:

Step1: Recall Line of Symmetry

A line of symmetry divides a figure into two mirror - image halves. For the letter 'H' - shaped figure, we check vertical and horizontal lines.

• A vertical line passing through the center of the horizontal bar and the middle of the vertical bars will divide the figure into two mirror - image halves.
• A horizontal line passing through the center of the vertical bars and the middle of the horizontal bars will also divide the figure into two mirror - image halves.

Step2: Draw the Lines

We draw one vertical line (along the vertical axis of symmetry) and one horizontal line (along the horizontal axis of symmetry) through the center of the 'H' - shaped figure.

Question 16:

Step1: Recall Center of Symmetry

The center of symmetry is a point such that for every point \(P\) in the figure, there is a corresponding point \(P'\) such that the center is the mid - point of the segment \(PP'\).

Step2: Locate the Center

For the 'H' - shaped figure, the center of symmetry is the intersection point of the vertical and horizontal lines of symmetry (the mid - point of the figure, where the horizontal and vertical bars cross each other).

Question 17:

Step1: Recall Order and Magnitude of Symmetry

• The order of rotational symmetry is the number of times a figure can be rotated about its center of symmetry and still look the same within a full rotation (\(360^{\circ}\)).
• The magnitude of rotational symmetry is the smallest angle through which the figure can be rotated to coincide with itself.

Step2: Determine Order

For the 'H' - shaped figure, when we rotate it about its center of symmetry:

• A rotation of \(180^{\circ}\) will make it coincide with itself. Also, a rotation of \(360^{\circ}\) (which is the same as the original position) will also make it coincide. But the non - trivial rotations: we can rotate it \(180^{\circ}\) and \(360^{\circ}\), but the order is the number of distinct positions. The figure has rotational symmetry of order 2 (it can be rotated by \(180^{\circ}\) and \(360^{\circ}\), but \(360^{\circ}\) is the identity rotation. The number of times it maps onto itself in \(360^{\circ}\) is 2: at \(0^{\circ}\) (original) and \(180^{\circ}\)).

Step3: Determine Magnitude

The magnitude is the smallest angle of rotation for which the figure coincides with itself. Since it coincides with itself after a \(180^{\circ}\) rotation, the magnitude of rotational symmetry is \(180^{\circ}\).

Answer:

s:

1. Draw one vertical and one horizontal line through the center of the 'H' - shaped figure (along the axes of symmetry).
2. The center of symmetry is the intersection point of the vertical and horizontal lines of symmetry (the mid - point of the 'H' - shaped figure).
3. The order of rotational symmetry is 2, and the magnitude of rotational symmetry is \(180^{\circ}\).