Question

1. reflecting the heart over line a then reflecting over line d is equivalent to what rotation?
2. reflecting the l - shaped figure over line l then reflecting over line m is equivalent to what rotation?

Explanation:

Problem 5

Step1: Recall reflection-rotation relation

When a figure is reflected over two intersecting lines, the composition of the two reflections is a rotation about the point of intersection of the lines. The angle of rotation is twice the angle between the two lines.

Step2: Identify angle between lines

The angle between line \(a\) and line \(d\) is \(70^\circ\).

Step3: Calculate rotation angle

The rotation angle is \(2\times70^\circ = 140^\circ\) about point \(p\).

Step1: Recall reflection-rotation relation

For two intersecting lines, the composition of two reflections over them is a rotation about their intersection point. The rotation angle is twice the angle between the lines.

Step2: Identify angle between lines

The angle between line \(l\) and line \(m\) is \(85^\circ\).

Step3: Calculate rotation angle

The rotation angle is \(2\times85^\circ=170^\circ\) about point \(C\).

Answer:

A rotation of \(140^\circ\) about point \(p\)

Problem 6