Question

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

Answer 1

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:

$W=(\frac{7+13}{2},\frac{2+13}{2})=(10,7.5)$

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:

$\begin{gathered} 10=\frac{3+x_1}{2} \\ \text{solving:} \\ x_1=2\cdot10-3 \\ x_1=17 \end{gathered}$

Also in the y-coordinates:

$\begin{gathered} 7.5=\frac{12+x_2}{2} \\ \text{Solving:} \\ x_2=2\cdot7.5-12 \\ x_2=3 \end{gathered}$

So bring the shovels to the point (17,3).