Diameter of a circle question!Help please!?

Question

These are the last few questions that I need help with to help my Grandson. Thankyou so much! Best answer will get the points!

The diameter of a circle joins the points( -1, -6) and (3, 9). Where is the centre of the circle located and what is the radius?

Answer 1

Hi,

The center is the midpoint of the 2 ends of the diameter, so average the x values and average the y values.

For x, (-1 + 3)/2 = 1

For y, (-6 + 9)/2 = 1.5

So the center is at (1,1.5)

To find the radius, use the distance formula from the center to either end of the diameter. We will find the distance from (1,1.5) to (3,9). The distance formula is:

Distance = √[(X2 - X1)² + (Y2 - Y1)²]

If we let X1 = 1, Y1 = 1.5, X2 = 3, and Y2 = 9 then

Distance = √[(3 - 1)² + (9 - 1.5)²] = √[(2)² + (7.5)²] = √4+ 56.25
= √60.25 = 7.762


The center is at (1,1.5) and the radius is about 7.762.



I hope that helps!! :-)

Answer 2

The diameter is the line across the circle going through the center. The center is the midpoint of this line. All you have to do is find out what the midpoint is of the line between (-1, -6) and (3,9). This is relatively straightforward:

The midpoint of a line defined by points (x1,y1) and (x2,y2) is the point (x3,y3) such that 'x3 = ((x1+x2)/2)' and 'y3= (y1+y2)/2'. In other words the midpoint's x-coordinate is simply the x-coordinate falling half-way between the first points x-coordinate and the last points x-coordinate. The same applies for the y-coordinate. With this knowledge we can find the center of the circle:

The coordinates of the center will be:
x-coordinate = (-1+3))/2
= (2)/2
= 1
= 2
y-coordinate = (-6+9)/2
= (3)/2
= 3/2
= 1 1/2

So the center is at (1, 1 1/2). And that's your answer, I hope this helps. Follow the link under 'sources' for a more detailed explanation of midpoint and the midpoint formula. I hope this helps.

Answer 3

The centre of the circle is the mid-point of the line joining (-1, -6) and (3, 9).
That has an x co-ordinate equal to the average of -1 and 3, which is (3 + (-1))/2 = 1, and a y co-ordinate equal to the average of -6 and 9, which is ((-6) + 9)/2 = 3/2. The centre is therefore (1, 3/2).

The radius is half the length of the line joining these two points. Using Pythagoras theorem, that is:
(1/2) sqrt( (9 - (-6))^2 + (3 - (-1))^2 )
= (1/2) sqrt(15^2 + 4^2)
= (1/2) sqrt(225 + 16)
= (1/2) sqrt(241)
= 7.76.

Answer 4

Assuming those points are the endpoints of the diameter, the center is at (1, 1.5) which is the midpoint of (-1, -6) and and (3, 9). The diameter of your circle is therefore 15.524 of whatever units you are using. The radius is half of that, or 7.7621.

Answer 5

Draw a triangle:

y side = 6+9 =15
x side= 3+1 = 4

15^2 + 4^2 = r^2
radius= 241^1/2

the center is (x=1, y=1.5)

Answer 6

the center is the midpoint of the two pts shown, so add x1 and x2 together and divide by 2 and add y1 and y2 and divide by two making the midpoint (1, 3/2) the radius is the distance between the midpoint and one of the points and that is the sqaure root of (x2-x1)squared plus (y2-y1)squared the radius is

Answer 7

you don't have enough info.
If it was mentioned that the given two points were actually on the circle, then the center is at the middle of the line, ie (1, 1.5)