To find the coordinates of point T, we can use the midpoint formula and knowledge of coordinate geometry. The midpoint formula states that given two points \(\((x_1, y_1)\)\) and \(\((x_2, y_2)\)\), the coordinates of the midpoint \(\(M\)\) are:
\(\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]\)
In this problem:
- The midpoint \(\(M\)\) is given as \(\((2.15, 10.7)\)\).
- Point \(\(U\)\) is given as \(\((13.7, 14.5)\)\).
- Let the coordinates of point \(\(T\)\) be \(\((x_1, y_1)\)\).
We can use the midpoint formula and rearrange it to solve for \(\(x_1\)\) and \(\(y_1\)\).
\(\[
\left( \frac{x_1 + 13.7}{2}, \frac{y_1 + 14.5}{2} \right) = (2.15, 10.7)
\]\)
From the x-coordinates:
\(\[
\frac{x_1 + 13.7}{2} = 2.15
\]\)
Multiply both sides by 2:
\(\[
x_1 + 13.7 = 4.3
\]\)
Subtract 13.7 from both sides:
\(\[
x_1 = 4.3 - 13.7
\]\)
\(\[
x_1 = -9.4
\]\)
From the y-coordinates:
\(\[
\frac{y_1 + 14.5}{2} = 10.7
\]\)
Multiply both sides by 2:
\(\[
y_1 + 14.5 = 21.4
\]\)
Subtract 14.5 from both sides:
\(\[
y_1 = 21.4 - 14.5
\]\)
\(\[
y_1 = 6.9
\]\)
Thus, the coordinates of point \(\(T\)\) are \(\((-9.4, 6.9)\)\).
So,
\(\[ T = (-9.4, 6.9) \]\)
