In the video you used two circles that had the same radius. But you don't really need to have the radii equal to each other, do you?

Actually, just looked at the hints for the problem (which does not use two congruent circles): ``` How can you guarantee that a line is perpendicular? If we pick two points on the perpendicular line which are an equal distance from the intersection, they will also be the same distance from every other point on the line we started with. If we don't already have the perpendicular line, is there another way to find the blue points? If we use the compass to put a circle somewhere on the line, the circle will include all points that are the same distance from that point, including the two blue points. We can add a second circle somewhere else on the line that intersects with the first circle. ```

what is arbitrary point?

Arbitrary just means random, so an arbitrary point is a point that is marked somewhere without much consideration. In this case, it would have to be on the paper and you would not want it too close to the line or the ends of the line, but that leaves a lot of space to put it in.

Can you guess where the line will be, without useing circles?

Constructions are very precise, guessing may only give an approximate answer. You do not need full circles, just arcs where both sides intersect.

Where are the Construction Problems?

Unfortunately, there are none on KA. They should really make some though.

Main content

High school geometry

Course: High school geometry > Unit 3

Lesson 8: Constructing lines & angles

Geometric constructions: perpendicular line through a point on the line

Name: Geometric constructions: perpendicular line through a point on the line
Uploaded: 2013-08-15T15:19:28Z
Description: Sal constructs a line perpendicular to a given line through a point on the line using compass and straightedge.

CCSS.Math:

HSG.CO.D.12

Google Classroom

Sal constructs a line perpendicular to a given line through a point on the line using compass and straightedge. Created by Sal Khan.

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Christi
Posted 10 years ago. Direct link to Christi's post “In the video you used two...”
In the video you used two circles that had the same radius. But you don't really need to have the radii equal to each other, do you?
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(16 votes)
Answer
- Christi
  Posted 10 years ago. Direct link to Christi's post “Actually, just looked at ...”
  Actually, just looked at the hints for the problem (which does not use two congruent circles):
  
  How can you guarantee that a line is perpendicular? If we pick two points on the perpendicular line which are an equal distance from the intersection, they will also be the same distance from every other point on the line we started with. If we don't already have the perpendicular line, is there another way to find the blue points? If we use the compass to put a circle somewhere on the line, the circle will include all points that are the same distance from that point, including the two blue points. We can add a second circle somewhere else on the line that intersects with the first circle.
  Comment on Christi's post “Actually, just looked at ...”
  (8 votes)
Jeffy Cherian
Posted 9 years ago. Direct link to Jeffy Cherian's post “When constructing paralle...”
When constructing parallel lines with a compass and straightedge, how should you start the construction?
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(3 votes)
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Mark Wilson
Posted 4 years ago. Direct link to Mark Wilson's post “What software or app is t...”
What software or app is this with this compass & straight edge?
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(4 votes)
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- Duskpin
  Posted 7 months ago. Direct link to Duskpin's post “I am pretty sure it was e...”
  I am pretty sure it was embedded into the practice at the time.
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  (1 vote)
Chinmayee15
Posted 6 years ago. Direct link to Chinmayee15's post “what is arbitrary point?”
what is arbitrary point?
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(2 votes)
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- David Severin
  Posted 6 years ago. Direct link to David Severin's post “Arbitrary just means rand...”
  Arbitrary just means random, so an arbitrary point is a point that is marked somewhere without much consideration. In this case, it would have to be on the paper and you would not want it too close to the line or the ends of the line, but that leaves a lot of space to put it in.
  Button navigates to signup page
  (2 votes)
Philip Kujawa
Posted 5 years ago. Direct link to Philip Kujawa's post “Can you guess where the l...”
Can you guess where the line will be, without useing circles?
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(2 votes)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “Constructions are very pr...”
  Constructions are very precise, guessing may only give an approximate answer. You do not need full circles, just arcs where both sides intersect.
  Button navigates to signup page
  (2 votes)
SFAIRFIELD
Posted 7 years ago. Direct link to SFAIRFIELD's post “Where are the Constructio...”
Where are the Construction Problems?
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(2 votes)
Answer
- INonDeficere
  Posted 4 years ago. Direct link to INonDeficere's post “Unfortunately, there are ...”
  Unfortunately, there are none on KA. They should really make some though.
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  (2 votes)
PeterB
Posted 9 years ago. Direct link to PeterB's post “When I try the exercises ...”
When I try the exercises in "Compass constructions 1", my tools behave differently than Sal's. Specifically, my straightedge tool seems to only create line segments, not lines, which makes solving the problem I'm working on ("Copy an angle") extremely annoying. Does anyone else see this? Is there some user interface to change the straightedge mode that I'm overlooking?
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(2 votes)
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Haley Ellenburg
Posted 5 years ago. Direct link to Haley Ellenburg's post “I Haley and I'm in the 10...”
I Haley and I'm in the 10 I would have not thought of this math that they have this day
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(1 vote)
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- Duskpin
  Posted 7 months ago. Direct link to Duskpin's post “Oops, wrong tab, but grea...”
  Oops, wrong tab, but great thing to hear!
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  (1 vote)
louisaandgreta
Posted 15 days ago. Direct link to louisaandgreta's post “0:49 - 0:56 Can someone c...”
0:49
-
0:56
Can someone clarify how we know that those points, where the two circles intersect, are equidistant from both of these centers that sal just constructed?

It’s obviously because of the radius but I couldn’t explain it or prove it, and as Sal tells us we shouldn’t just rely on what we see on the figure since it might be to scale or something.
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(1 vote)
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GarciaJoanne69
Posted 7 years ago. Direct link to GarciaJoanne69's post “How do i do this problem ...”
How do i do this problem algebra bisects ? m<ABX=5x,m <XBC=3x+10
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(1 vote)
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Video transcript

Construct a line perpendicular to the given line. So if I can pick two arbitrary points on this line, and if I can make a line that is always equidistant from those two points, then that line will be perpendicular. And actually, it will be a perpendicular bisector of the segment formed by those two points. Now, they don't care whether we're bisecting anything. But they do care about it being perpendicular. So let's do this. So I'm going to draw a circle with my compass. And so let's just pick that point right over there. I could adjust the radius if I like. But I might as well-- well, I'll just leave it right over there. Now let me draw another circle. And this time, I'm going to center it where the first circle intersects with my line. And then I'm going to adjust the radius to overlap with the first dot. And now, where these two circles intersect, those are points that are equidistant from both of these centers that I just constructed. So let me draw a line that connects those two. And that line is going to be perpendicular to our original line.