Question

If T is the midpoint of Su find the values of x and ST. The diagram is not to scale.ST9x4x + 25O x = 10, ST = 45O x = 5, ST = 60O x = 10, ST = 60O x = 5. ST = 45

Answer 1

hello

the question given involves the midpoint of a line

since t is the mid point of the line, we can equate both sides

what this implies is that st is equal to tu

$\begin{gathered} st=tu \\ 9x=4x+5 \\ \end{gathered}$

now we solve for x

$\begin{gathered} 9x=4x+5 \\ 9x-4x=5 \\ 5x=5 \\ \text{divide both sides by 5} \\ \frac{5x}{5}=\frac{5}{5} \\ x=1 \end{gathered}$

now we have x = 1

we can substitute x = 1 in both st and tu

in st

$\begin{gathered} st=9x \\ x=1 \\ st=9(1)=9 \end{gathered}$

in tu

$\begin{gathered} tu=4x+5 \\ tu=4(1)+5 \\ tu=4+5 \\ tu=9 \end{gathered}$

from the calculations above, x = 1, st = 9 and tu = 9