the mid-point of the line FG is (6,10). if the coordinates of G is (8,14) find the coordinates of F.
There are a number of ways to solve this but I think the simplest is to use the definiton of midpoint.
We know mdpt(FG) = 1/2(F+G) where FG is the segement and F,G denote the points, i.e. coordinates. Thus (6,10) = 1/2(x+8,y+14)
Now solve for each coordinate. Let us know if you need further assistance, but please show your work too.
I don't know
(7,4)
We can start by substituting the coordinates of the midpoint (6,10) and the coordinates of point G (8,14) into the midpoint formula, which is (x1 + x2)/2 and (y1 + y2)/2 for the x-coordinate and y-coordinate respectively.
Using the x-coordinate:
(6,10) = (x + 8)/2
Multiplying both sides of the equation by 2:
12 = x + 8
Subtracting 8 from both sides of the equation:
4 = x
So, the x-coordinate of point F is 4.
Using the y-coordinate:
(6,10) = (y + 14)/2
Multiplying both sides of the equation by 2:
12 = y + 14
Subtracting 14 from both sides of the equation:
-2 = y
So, the y-coordinate of point F is -2.
Therefore, the coordinates of point F are (4, -2).