We are given the coordinates of the points:
T(3,12) U(7,2) V(13,13)
We must find the coordinates of a point X where a treasure is to be found.
The first instruction is to find the midpoint of UV and call it W. The midpoint is calculated as follows:
[tex]W=(\frac{7+13}{2},\frac{2+13}{2})=(10,7.5)[/tex]We know point W is in the middle of T and X. That is why TX is twice TW. We must now find the coordinates of X. Let's call them (x1,x2).
Since W is the midpoint of TX:
[tex]\begin{gathered} 10=\frac{3+x_1}{2} \\ \text{solving:} \\ x_1=2\cdot10-3 \\ x_1=17 \end{gathered}[/tex]Also in the y-coordinates:
[tex]\begin{gathered} 7.5=\frac{12+x_2}{2} \\ \text{Solving:} \\ x_2=2\cdot7.5-12 \\ x_2=3 \end{gathered}[/tex]So bring the shovels to the point (17,3).