Question

suppose m is the mid - point of fg. if fm = 6x - 9 and mg = 4x + 3, find the value of x and fg. x = fg =

Explanation:

Step1: Use mid - point property

Since M is the mid - point of FG, then FM = MG. So we set up the equation 6x−9 = 4x + 3.

Step2: Solve for x

Subtract 4x from both sides: 6x−4x−9=4x−4x + 3, which simplifies to 2x−9 = 3. Then add 9 to both sides: 2x−9 + 9=3 + 9, getting 2x = 12. Divide both sides by 2: $\frac{2x}{2}=\frac{12}{2}$, so x = 6.

Step3: Find FG

Since FG=FM + MG and FM = MG, FG = 2FM (or 2MG). First, find FM when x = 6. FM=6x−9=6×6−9=36−9 = 27. Then FG = 2×27=54.

Answer:

x = 6, FG = 54