# Thread: Mid point of a line segment

1. ## Mid point of a line segment

This is the question I am trying to solve:

A circle has centre (-1,8). If a diameter is GH and G=(3,-2), calculate the coordinates of H.

I drew a circle with the centre as (-1,8) and G as a point on the circle as (3,-2) but I don't know what to do next.

2. Hi!paulo1913.
Here is the solution.
Centre of the circle will be the midpoint of GH. Let coordinate of H be (x,y) then
(3+x)/2=-1
solving it we get x=-5
similarly (-2+y)/2=8
solving this we get y=18
hence the coordinate of H are (-5,18)

3. Originally Posted by Paulo1913
This is the question I am trying to solve:

A circle has centre (-1,8). If a diameter is GH and G=(3,-2), calculate the coordinates of H.

I drew a circle with the centre as (-1,8) and G as a point on the circle as (3,-2) but I don't know what to do next.

I know you said you already drew a picture but I think that this image might help. Consider the slope.

Hope this helps.

4. Thank you very much for the help. Could you help me with this question?

Show that the midpoint of the line segment joining (6,-1) and (-3,8) lies on the line y=-5x+11

I figured out that the coordanates are (1.5,3.5) but I am not sure how that helps show the equation....

5. Originally Posted by Paulo1913
Thank you very much for the help. Could you help me with this question?

Show that the midpoint of the line segment joining (6,-1) and (-3,8) lies on the line y=-5x+11

I figured out that the coordanates are (1.5,3.5) but I am not sure how that helps show the equation....
New and unrelated questions require new threads.

Substitute x = 1.5 into the equation for the line. Do you get y = 3.5 ....

6. Is that all that is required to prove that it lies on the line?

7. Originally Posted by Paulo1913
Is that all that is required to prove that it lies on the line?
Yes.