How do I find the coordinates of the centre and vertices in a square and circle?

  • Context: MHB 
  • Thread starter Thread starter Maths student
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around finding the coordinates of the center and vertices of a square and a circle, including specific calculations related to given points and equations. The scope includes mathematical reasoning and problem-solving related to geometry.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a problem involving a square with vertex A at (6, -4) and a diagonal BD defined by the equation 2y - x = 6, asking for the coordinates of the center and other vertices.
  • Another participant suggests finding the line perpendicular to BD that contains A to assist in solving part 1a.
  • For part 2, a participant provides a hint regarding the equation of a circle and suggests forming equations by substituting the given points into the circle's equation.
  • One participant proposes an alternative method for part 2, suggesting the use of perpendicular bisectors to find the center of the circle defined by points O, A, and B.
  • Another participant expresses frustration with rote learning and seeks clarification on how to approach the problems, particularly part b and part 2.
  • A participant shares their experience of passing with rote learning, indicating a lack of understanding of the underlying concepts, and requests detailed working steps for clarity.
  • Concerns are raised about the effectiveness of rote learning in mathematics, with an emphasis on understanding concepts rather than memorizing methods.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness of rote learning versus understanding mathematical concepts. There is no consensus on the best approach to solving the problems presented, and some participants are unsure about the methods to use.

Contextual Notes

Participants mention limitations such as not being able to use calculators and the need for specific working steps to understand the problem-solving process. There are also references to the nature of exam preparation and the repetition of questions in exams.

Who May Find This Useful

This discussion may be useful for students preparing for exams in geometry, particularly those struggling with understanding the concepts of coordinates, circles, and squares, as well as those interested in different approaches to problem-solving in mathematics.

Maths student
Messages
3
Reaction score
0
1) The vertex A if a square ABCD is at the point (6, -4 ) . The diagnol BD has equation 2y-x=6, and the vertex B is nearer to the origin than D.

a)calculate the coordinates of the centre of the square.

b)calculate the coordinates of B and C.



2) Calculate the coordinates of the centre of the circle that pass through (0,2) , (4,8) and the origin O.



I attempted 1a and 2 and got random answers... which were not on the answers page. I couldn't do b. pls can someone show me the actual working as i can figure the answer on the answers page anyways :P i need to know how to work these out - they're hard :/
 
Mathematics news on Phys.org
Maths student said:
1) The vertex A if a square ABCD is at the point (6, -4 ) . The diagnol BD has equation 2y-x=6, and the vertex B is nearer to the origin than D.

a)calculate the coordinates of the centre of the square.

b)calculate the coordinates of B and C.



2) Calculate the coordinates of the centre of the circle that pass through (0,2) , (4,8) and the origin O.



I attempted 1a and 2 and got random answers... which were not on the answers page. I couldn't do b. pls can someone show me the actual working as i can figure the answer on the answers page anyways :P i need to know how to work these out - they're hard :/

Hi Maths student! Welcome to MHB!

For 1a) how far can you get to find the line perpendicular to BD that contains A?

You will need the answer to 1a) to answer 1b).

For 2), hint: the equation of a circle is $(x-a)^2+(y-b)^2=r^2$, where $r$ is the radius, and (a,b) is the center.
What is the set of equations that you can get by substituting each of the given points for x and y?
 
For 2) let's denote $O(0,0)$, $A(0,2)$ and $B(4,8)$. As an alternative solution, you could find the intersection of the perpendicular bisectors to $OA$ and $OB$.
 
Can you help with b?

And how do you know how to do 2? Do I just rote learn the method.. I mean, is that what you did? I don't get it
 
Maths student said:
Can you help with b?

And how do you know how to do 2? Do I just rote learn the method.. I mean, is that what you did? I don't get it

Rote learning is a bad way to learn math. It's a dead end. Math is about understanding.
But you have come to the right place if you want to learn.
Still, we can only help you if you give us some indication what you know and/or what you are thinking.

So, if you're willing, what are your thoughts on 1a?
 
I passed last year with an A by rote learning the methods, for all I care. The questions repeat every year with different numbers.

I understood 1a, having been aught on another forum.

I have no clue in regards to b and for 2 I thought that if the same coordinate appearing means the line is the diameter... But obviously not.
I'm tired, it's late and the exam is tomorrow.
Fyi I can't use a calculator so using y minusyone equals mx plus c and the rule about the gradients and parrellr and perpendicular lines, please can you just show your working.

Fyi this isn't homework, just practice for the exam. The answers are in my textbook anyways. I just want to know how you het the answer.

Trust me I also got an A* last year despite teachers thinking I would struggle as I didn't really understand, but just rote learned info.
These exams are only testing your memory if you practice enough questions anyways :p
 

Similar threads

MHB Finding exact 3d coordinates in a falling pipe system with corners
  • · Replies 20 ·
Replies
20
Views
4K
Find the area of a segment of a circle using integration
  • · Replies 8 ·
Replies
8
Views
2K
High School How Can I Find the Centre Point of a Circle with Given Coordinates and Radius?
  • · Replies 5 ·
Replies
5
Views
3K
MHB Approximating Trig Values using the Unit Circle
  • · Replies 11 ·
Replies
11
Views
3K
MHB How do I use the midpoint formula to find the coordinates of point C?
  • · Replies 2 ·
Replies
2
Views
6K
Undergrad Did I figure-out z-translation of 2D-coordinates correctly?
  • · Replies 4 ·
Replies
4
Views
3K
MHB How Do You Find the Equation of a Line Through a Point and a Circle's Center?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Finding Coordinates on a circle with time/speed
  • · Replies 3 ·
Replies
3
Views
7K
MHB How do I calculate the side of a rhombus using the bisector of an angle theorem?
  • · Replies 1 ·
Replies
1
Views
2K
MHB How do I calculate the center of a square given its position and orientation?
  • · Replies 3 ·
Replies
3
Views
3K