Question

number 15, how can i find X? what does it mean by two times

Answer 1

Given the coordinates of T, U and V as;

$T(3,12),U(7,2),V(13,13)$

The midpoint of UV is W, which is;

$\begin{gathered} W=(\frac{7+13}{2},\frac{2+13}{2}) \\ W=(\frac{20}{2},\frac{15}{2}) \\ W=(10,7.5) \end{gathered}$

Also, W is collinear and between T and X;

Sketching the graph here for clarity, we have;

Also, TX is exactly two times TW;

That means, W is the midpoint of TX, we have;

$\begin{gathered} (10,7.5)=(\frac{3+x}{2},\frac{12+y}{2}) \\ \frac{3+x}{2}=10 \\ 3+x=20 \\ x=20-3 \\ x=17 \\ \text{Also;} \\ \frac{12+y}{2}=7.5 \\ 12+y=15 \\ y=15-12 \\ y=3 \end{gathered}$

Hence, the coordinate of X is;

$X(17,3)$