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=((7+13)/(2),(2+13)/(2)) \\ W=((20)/(2),(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)=((3+x)/(2),(12+y)/(2)) \\ (3+x)/(2)=10 \\ 3+x=20 \\ x=20-3 \\ x=17 \\ \text{Also;} \\ (12+y)/(2)=7.5 \\ 12+y=15 \\ y=15-12 \\ y=3 \end{gathered}`

Hence, the coordinate of X is;

`X(17,3)`