What is the length of FH if G is the midpoint, FG=12x-5, GH = 7x?
Point G lies between points F and H on .
If the length of FH is 18 units, what is the value of x?
To find the length of FH, we need to determine the value of x. Once we have found the value of x, we can substitute it back into the expression for GH to find its length.
Given that G is the midpoint of FH, we can use the Midpoint Formula. According to the Midpoint Formula, the coordinates of the midpoint (G) are the average of the coordinates of the endpoints (F and H). In this case, we are given that FG = 12x - 5 and GH = 7x.
Using the Midpoint Formula, we can write the equation:
(12x - 5 + 7x) / 2 = 0
Simplifying the equation:
(19x - 5) / 2 = 0
By multiplying both sides of the equation by 2:
19x - 5 = 0
Adding 5 to both sides of the equation:
19x = 5
Dividing both sides of the equation by 19:
x = 5/19
Now that we have the value of x, we can substitute it into the expression for GH to find its length:
GH = 7x
GH = 7 * (5/19)
GH = 35/19
Therefore, the length of FH is GH, which is 35/19.
Then FG=GH
12x-5=7x
solve for x, then FH (12x-5+7x)