Question

Can you help me find the circumcenter of this triangle? The vertices of triangle are A(2,2), B(4,10), and C(12,2).

Answer 1

Do you know how to find midpoint?

Answer 2

Yes, I have found the midpoint already.

Answer 3

Ok, of two sides? What are they so we can make some equations

Answer 4

okay I did the midpoint of A and B which is (3,6)

Answer 5

Alright we need one more so wanna do the midpoint of BC?

Answer 6

So it would be 4+12/2=8 and 10+2/2=6 so the midpoint is (8,6) right?

Answer 7

Yep, now we need to find the slope of AB and BC

Answer 8

So we would have to do y2-y1 and x2-x1?

Answer 9

the slope of AB= (8,2)

Answer 10

and the slope of BC= (-8,8) i think?

Answer 11

Slope isn't a coordinate.

10-2/4-2
8/2
4

slope of AB is 4

Answer 12

Oh okay so the slope of BC= -8/8

Answer 13

Yes so -1.

so slope of AB is 4, midpoint of AB is (3,6)

we need the slope of the perpendicular bisector of ab so we change the sign, and flip it

4 turns into -1/4

now we put this into point slope form

y-6=-1/4(x-3)

wanna simplify that so its in slope intercept form?

Answer 14

Yes

Answer 15

So do we solve for y?

Answer 16

Yep isolate y on the left

y-6=(-1/4)x+3/4

y=(-1/4)x+27/4

ok keep that equation for a second, do the same thing with BC

slope=-1
midpoint=(8,6)

Answer 17

So y-6=(-1)x+8

Answer 18

Okay, you lost me there. Before I got here, I made it to the point slope form and then got lost. How did you get the 3/4 in y-6=(-1/4)x+3/4? And How did it change to 27/4? And what am I supposed to do after I solve for y?

Answer 19

Okay so what do we have to do now?

Answer 20

Figure out what x and y are, which are the coordinates for the circumcenter.

do you know how to solve a system of equations?

Answer 21

No i mean you have two equations, two variables in each and you have to find out what each variable is