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

[Maths student]

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 :/

 

[I like Serena]

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?

 

[Evgeny.Makarov]

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 $OB$.

 

[Maths student]

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

 

[I like Serena]

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?

 

[Maths student]

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