I am trying to find the coordinates of a point in a line. I have one end, and I have the midpoint. What formula should I use to find the one on the end?
The one end is (8,4) and the MIDPOINT is (14, 7). What would I do to find the opposite point?!
thanks!
(8,4) (14,7) (x, y)
x - 14 = 14 - 8
x = 20
y -7 = 7 - 4
y = 10
(20,10)
To find the coordinates of the other end of the line, you can use the midpoint formula. The midpoint formula states that the midpoint of a line segment, when given the coordinates of both ends, can be found by calculating the average of the x-coordinates and the average of the y-coordinates.
The formula is:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
In your case, you have one end of the line coordinates as (8, 4) and the midpoint as (14, 7). Let's call the coordinates of the other end as (x, y).
Using the midpoint formula, we can set up the following equations:
[(8 + x)/2, (4 + y)/2] = (14, 7)
Now, simplify the equation by expanding the terms:
[(8 + x)/2] = 14
[(4 + y)/2] = 7
Next, solve for x and y by cross-multiplying and simplifying:
8 + x = 28
4 + y = 14
Solving for x and y individually:
x = 28 - 8
y = 14 - 4
x = 20
y = 10
Therefore, the coordinates of the other end of the line are (20, 10).