Question

Х m . In the segment shown point M is the mi M the midpoint of AB. Given AM = 3x+ 12 and MB = MB = 5x -4, find the length of AM. DP A M B M

Answer 1

From the information provided, M is the midpoint of line segment AB. This implies that the segments AM and MB are two equal halves of the entire length,

Therefore, we would have the following;

$\begin{gathered} AM+MB=AB \\ \text{Also,} \\ AM=MB \\ \text{Where;} \\ AM=3x+12,MB=5x-4 \\ We\text{ now have;} \\ 3x+12=5x-4 \\ \text{Collect all like terms;} \\ 12+4=5x-3x \\ 16=2x \\ \text{Divide both sides by 2;} \\ \frac{16}{2}=\frac{2x}{2} \\ 8=x \end{gathered}$

Where AM = 3x+12, we now have;

$\begin{gathered} AM=3x+12 \\ AM=3(8)+12 \\ AM=24+12 \\ AM=36 \end{gathered}$

ANSWER:

Segment AM = 36