Question

1. triangle figure 19. two squares figure 18. insert the reply a. reflection over a vertical line that passes through the point where the figures intersect b. a rotation of 90° about the point where the figures intersect c. a rotation of 180° about the point where the figures intersect d. a rotation of 120° about the point where the figures intersect e. reflection over a horizontal line that passes through the center of both figures

Explanation:

Problem 18 (Assuming it's about reflecting the triangle)

Step1: Identify reflection axis

For a triangle (isosceles or equilateral, as drawn), a vertical line through the vertex (top) and midpoint of the base is the axis of symmetry.

Step2: Reflect the triangle

Using the vertical line through the vertex, mirror each point of the triangle across this line. The reflected triangle will be congruent, with the left and right sides swapped relative to the axis.

Problem 19 (For the two squares intersecting)

Step1: Analyze transformation

The two squares intersect at a point. A rotation about that intersection point by \(90^\circ\) (since squares have \(90^\circ\) rotational symmetry) will map one square to the other. Let's check the options:

• Option A: Reflection over a vertical line through intersection – squares might not be symmetric over vertical here.
• Option B: Rotation of \(90^\circ\) about intersection – matches square's rotational symmetry.
• Option C: \(180^\circ\) rotation – would flip more, not matching the diagram.
• Option D: \(270^\circ\) rotation – similar to \(90^\circ\) but direction, but \(90^\circ\) is more likely.
• Option E: Reflection over horizontal line – unlikely as per diagram.

Answer:

(for Problem 19):
B. a rotation of \(90^\circ\) about the point where the figures intersect

(Note: For Problem 18, if it's a reflection, the answer would involve drawing the reflection over the vertical line through the triangle's vertex. Since the exact question for 18 is unclear from the image, but assuming reflection, the process is as above. For Problem 19, the correct option is B as explained.)