Question

a. for the figure to the right, use any construction method to find the image of δabc if δabc is reflected in l to obtain δabc and then δabc is reflected in m to obtain δabc (l and m intersect at o)
b. conjecture what single transformation will take δabc directly to δabc
c. answer the questions in (a) and in (b) for the case in which l and m are perpendicular
what single transformation will take δabc directly to δabc when l is perpendicular to m?
a. a full turn about o
b. a quarter - turn counterclockwise about o
c. a quarter - turn clockwise about o
d. a half - turn about o

Explanation:

When a figure is reflected over two intersecting lines \(L\) and \(m\) (intersecting at \(O\)), the composition of two reflections is a rotation. The measure of the rotation angle is \(2\theta\), where \(\theta\) is the angle between the two lines \(L\) and \(m\). If \(L\perp m\), then \(\theta = 90^{\circ}\), and the rotation angle \(2\theta=180^{\circ}\). A rotation of \(180^{\circ}\) about a point \(O\) is called a half - turn about \(O\).

Answer:

D. A half - turn about \(O\)