
Payne, Daniya

SY-24-24_Geometry_10_TWA_1

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Question

Brittni is using a compass and straightedge to construct the perpendicular bisector of 𝐽⁢𝐾¯. Her first steps are shown below.

Which picture correctly shows the next steps in the construction?

Responses

Image with alt text:

Image with alt text:

Image with alt text:

It looks like Brittni is in the process of constructing the perpendicular bisector of a line segment \( JK \) using a compass and straightedge, and the task is to identify the next correct step from images provided.

To guide you on what the correct next step should be, here’s a general outline of the steps involved in constructing a perpendicular bisector:

1. **Initial Setup**: The first step involves placing the compass point on one endpoint of the line segment \( JK \) (either \( J \) or \( K \)) and drawing an arc above and below the line. Without changing the compass width, repeat the same from the other endpoint, ensuring the arcs intersect above and below the line segment.

2. **Identifying Intersection Points**: The next step involves marking the intersection points of the arcs that are above and below the line segment. 

3. **Drawing the Perpendicular Bisector**: Using a straightedge, draw a line through the two points of intersection of the arcs. This line is the perpendicular bisector of \( JK \).

From the description you provided, it appears you need to choose the image that correctly shows the third step—drawing the line through the intersections of the arcs.

If you can access the images or describe them, I can help you choose the correct one based on the construction steps outlined.

Would you like further details on this construction, or do you have any other questions?

Here are 5 related questions to explore further:

1. How do you ensure the compass width remains unchanged when drawing arcs for the perpendicular bisector?
2. What are some common mistakes to avoid when constructing a perpendicular bisector?
3. Why is it important to use a compass and straightedge for geometric constructions rather than measuring tools?
4. Can you construct a perpendicular bisector without using a compass?
5. How can the concept of a perpendicular bisector be applied in real-world scenarios?

**Tip:** Always ensure that the compass width is more than half the length of the line segment to ensure the arcs intersect correctly above and below the segment.

Learn how to construct the perpendicular bisector of line segment JK using compass and straightedge with our step-by-step guide. Understand the process from initial setup to drawing the perpendicular bisector. Suitable for Grades 7-9 students learning geometric constructions.

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