Point H is the midpoint I'd line segment GJ
Line segment GH is 7x-5 HJ is 4x+1 what is the value of X?
To find the value of x, we can use the fact that H is the midpoint of line segment GJ.
The midpoint of a line segment is the average of the coordinates of the endpoints.
In this case, GJ is divided into two line segments: GH and HJ.
Let's write the equation for the midpoint.
The x-coordinate of the midpoint H is (x-coordinate of G + x-coordinate of J) / 2.
Similarly, the y-coordinate of the midpoint H is (y-coordinate of G + y-coordinate of J) / 2.
Let's substitute the given expressions for GH and HJ and solve for x.
For the x-coordinate:
(x-coordinate of G + x-coordinate of J) / 2 = x-coordinate of H
Substituting:
(7x - 5 + 4x + 1) / 2 = 7x - 5
Simplifying:
(11x - 4) / 2 = 7x - 5
Multiply both sides by 2 to get rid of the denominator:
11x - 4 = 14x - 10
Subtract 11x from both sides:
-4 = 3x - 10
Add 10 to both sides:
6 = 3x
Divide both sides by 3:
x = 2
Therefore, the value of x is 2.
To find the value of x, we can use the fact that point H is the midpoint of line segment GJ. This means that the lengths of GH and HJ are equal.
Let's set up the equation using the given lengths:
GH = HJ
Substituting the given expressions for GH and HJ:
7x - 5 = 4x + 1
Now, let's solve for x:
First, we can simplify the equation by combining like terms:
7x - 4x = 1 + 5
This simplifies to:
3x = 6
Now, divide both sides of the equation by 3 to isolate x:
3x/3 = 6/3
The equation becomes:
x = 2
Therefore, the value of x is 2.