Question

Kathy uses the following steps to construct a perpendicular line through a point C on a line segment:

Step 1: From point C, draw two arcs intersecting the line segment in points A and B.
Step 2: Using slightly more compass width, draw two arcs from point A, one above and the other below the line segment.
Step 3: Using the same width of the compass, draw two arcs from point B, above and below the line segment.
Step 4: Label the point of intersection of the arcs above the line segment as F and below the line as E.
Step 5: Using a compass, join E and F.

Answer 1

Part A: Which is the first incorrect step?
Part B: Using complete sentences, explain your answer for Part A.
Part C: Explain why a compass works for the construction done by Kathy.

Answer 2

I need someone to check my answer!

Answer 3

Step 1 is written incorrectly. It does not say to use a compass to draw the arcs. Plus, it assumes that points A and B are already on the line, but they are not. You mark points A and B after intersecting the arcs with the line segment. Normally, the point that is already on the line should be point A instead of C. Which makes this even more incorrect.

Steps 2 and 3 are correct.

Step 4 says to label the points of intersection of the arcs as F and E. However, there is no point D, so why isn't point D used? This does not mean that this is an incorrect step though.

Step 5 says to use a compass to connect the intersecting arcs. You do not use a compass for that. Straightedges are used to draw straight lines. Plus, it does not say to make a line segment, it says to join the points, which does not necessarily mean to join the points with a line segment.

The incorrect steps are steps 1, and 5. The first incorrect step is of course step 1. Kathy must have put points A and B on the line BEFORE making the arcs instead of AFTER making the arcs.

Answer 4

@ganeshie8
@thomaster

Answer 5

Step1 is fine
the first incorrect step is Step 5

Answer 6

Oh, ok. Is my explanation for step 5 good?

Answer 7

Step 5 says to use a compass to connect the intersecting arcs. You do not use a compass for that. Straightedges are used to draw straight lines. Plus, it does not say to make a line segment, it says to join the points, which does not necessarily mean to join the points with a line segment.

Answer 8

And if you could also help me with part c?

Answer 9

start something like this :
compass works because kathy;s construction involves drawing several arcs...

Answer 10

A compass works because it involves drawing arcs in order to make the perpendicular lines. Arcs must be drawn above and below the line, and each arc must be located at the right place. A compass can help you draw each arc in the right location. Arcs are needed in order to make perpendicular lines.

Answer 11

Eh, this is all I got ...

Answer 12

looks good to me!

Answer 13

Thank you! :)