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Question

Line segment RS has endpoints R(12,22) and S(52, -12) and is the radius of a circle.

a) If point R is the centre of the circle then determine the other endpoint of the diameter of the circle.

b) Calculate the diameter of the circle to the nearest tenth.

Answer 1

And find the slope of the line, and extend a line of the same slope and length from R to find the other endpoint.

a) slope = (-12 - 22)/(52 -12) = -30/40 = -3/4. Extending a line with the same slope and legth in the opposite direction can be done by going -40 units along x and 30 units along y. The other endpoint will then be (12 - 40, 22 -(-30)) or (-28, 52).
b) For this we find the distance between the two endpoints. D = sqrt((52-(-28))^2 + (-12-52^2)) = sqrt(80^2 + 60^2) = sqrt(6400 + 3600) = sqrt(100^2) = 10. The circle has a diameter of 10.

Answer 2

Let T be the other endpoint

Therefore R is the midpoint of the line since the diameter = 2* radius

(x+52)/2 = 12
x + 52 = 24
x = -28

(y+ (-12))/2 = 22
y - 12 = 44
y = 56

Then T = (-28, 56)

b) use the distance formula

sqrt ( (x1 - x2)^2 + (y1-y2)^2)

= sqrt( -28-52)^2 + (56+12)^2) = 104.9952

Diameter of the circle is approximately 105 units

Answer 3

Geez, this is an easy question. Very clearly you did not study and have absolutely no confidence in your ability to do math.

Let's call the point you want (X,Y)? Why, because I have to call it something.

Now we have a picture:

S'(X,Y) R(12,22) S(52,-12)

Because we have radius S'R and RS are the same length and one a line.

That means that we add the same "vector from S' to get to
R that we add to R to get S.
R-S' = S-R or ...
1)12-X = 52-12 => X = -52
2) 22-Y = -12 -22

So, X =-52 and Y = 12.

Now, if you knew how to calculate the length of a line, which again you obviously don't or don't believe you can, ...

the length is the square root of the squares of the difference of the two points or ... (pathagorus therem)
(52-12)*(52-12)+(22--12)(22--12) =(40*40)+(34*34) =

What ever this number is take the square root.

That's it.

Answer 4

finds the distance between then using the distance formula then times it by two in order to get the diameter.