Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 321

Loci and Construction

Here is a scale drawing of a room
The scale is 1cm to 2m

Link for image of drawing (Question 11); https://www.mathsgenie.co.uk/resources/4-loci-and-constructionans.pdf

In case link doesn’t work;

Image; a rectangle, corners marked A at the top left, B at the bottom left, C at the bottom right, and D at the top right.
A to D; 11cm
A to B; 5.5cm
I’m not sure if the dimensions are important or not.

A chair is going to be placed in the room
The chair must be closer to AB than BC
The chair must be less than 14m from D
Shade the region where the chair can be placed

*

I first worked out the scale of the distance from D, i.e, 7cm for the 14m.
Then set my compasses at 7cm and drew an arc to represent 14 m from D
I’m assuming the chair has to be placed somewhere in that region between D and the arc
But I’m puzzled regards the chair having to be closer to AB than BC
Does AB mean all the points on the line AB?
Does BC mean all the points on the line BC?
If so, is the point B on both lines AB, and BC?
As this comes under Loci and Construction I’m assuming I have to set my compasses in relation to AB / BC / and the arc I've drawn, and make some small arc marks?
Beyond that I’m stuck

---

Prioritise. Persevere. No pain, no gain.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 61

Re: Loci and Construction

Nearly there,
you drew the arc for the section less than 14m from D.

Now you need to draw the section that's closer to AB than BC. Is it a diagonal line?

The question is asking for the intersection or overlap between these two sections.

Yes AB just means the line AB, made up of every point on that line.

I suppose B would be on both AB and BC - meaning it's a tie for that point! Lol.

K_R

Last edited by Keep_Relentless (2024-05-09 01:30:18)

---

"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

paulb203

Member

Registered: 2023-02-24

Posts: 321

Re: Loci and Construction

Thanks.

I found out that I had to split the bottom left right angle into 2 45 degree angles, and draw a diagonal from there (point B)
Above that line is considered nearer AB, below it nearer BC.
I'm not sure I understand that though.

---

Prioritise. Persevere. No pain, no gain.

Keep_Relentless

Member

From: Queensland, Australia

Registered: 2024-05-05

Posts: 61

Re: Loci and Construction

Imagine drawing a line going right from anywhere on AB, until it touches the diagonal. And then from there, another line going down from the diagonal until it touches BC.

These two lines would be equal. Does that help at all? You can also fold the two sections on top of each other, so there's symmetry.

---

"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Loci and Construction

Sorry I've come late to this one.

Circle centre D, radius 14m is correct. Points must be inside the room and inside this circle.

To get points closer to AB than BC you need the line that is the angle bisecter of angle ABC. Why does that work?

Pick any point on the bisector. It is equidistant from AB and BC. So points above it will be closer to AB.

Note: The distance from a point to a line is defined as  the shortest so you go straight to the line, at right angles to the line.

So shade if in room, in circle and above line.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Loci and Construction

Sorry I've come late to this one.

Circle centre D, radius 14m is correct. Points must be inside the room and inside this circle.

To get points closer to AB than BC you need the line that is the angle bisecter of angle ABC. Why does that work?

Pick any point on the bisector. It is equidistant from AB and BC. So points above it will be closer to AB.

Note: The distance from a point to a line is defined as  the shortest so you go straight to the line, at right angles to the line.

So shade if in room, in circle and above line.

Bob

Bob,

1. Sorry to bother you again. Can you change my username? A member in another math group states that this username belongs to him and may be causing problems for me. I can think of a unique name that nobody else has.

2. I didn't do very well with this topic back in my school days. I never understood loci rules, geometric construction and geometric proofs.

Last edited by mathxyz (2024-05-10 07:35:09)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Loci and Construction

Check with the User list that our new name is unique and let me know what you'd like.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Loci and Construction

Check with the User list that our new name is unique and let me know what you'd like.

Bob

Bob,

How about any of the following new user names?

mathguy

mathdad

mathland

mathxyz

mathjoy

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Loci and Construction

I'm assuming you checked no username already exists. So choose.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Loci and Construction

I'm assuming you checked no username already exists. So choose.

Bob

How about mathxyz?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Loci and Construction

Done.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Loci and Construction

Done.

Bob

Yep. I love it. As a math nerd ?,  I had to include xyz.