Maths linear problem, need help finding working out (1 Viewer)

[Aeyis]

Given that one end of a diameter of a circle is ( 5, -1) and the centre of the circle is (0,4) find the other end of the diameter.

The answer is (-5, 5) I just dont know how to get there, can someone help out

 

[Nailgun]

You sure that's the answer? Might wanna double check that

Use distance formula to find radius of the circle = root(50)
Use gradient formula to find gradient of diameter line = -1

Hence find the equation of the circle x^2 + (y-4)^2 = 50
and the equation of the line y = -x +4

Equate the two to find points of intersection
Should get x = 5,-5
We have x = 5 already so we want x = -5
Sub into the line
We get P(-5,9)

I'm fairly sure that your answer is wrong lol

 

[Paradoxica]

The x values of the first endpoint, the centre, and the x value of the second endpoint are in an arithmetic progression.
The same is true for the corresponding y values.

 

[Nailgun]

The x values of the first endpoint, the centre, and the x value of the second endpoint are in an arithmetic progression.
The same is true for the corresponding y values.

Aaand this is the smart way to do it lol

 

[Nailgun]

you can see from the points plotted that the line between the first endpoint and your answer do not pass through the center of the circle

 

[RealiseNothing]

Given that one end of a diameter of a circle is ( 5, -1) and the centre of the circle is (0,4) find the other end of the diameter.

The answer is (-5, 5) I just dont know how to get there, can someone help out

Looking at the x-values:

5, 0, x

Looking at the y-values:

-1, 4, y

Just finish the pattern to get x=-5 and y=9 so (-5,9).