# How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-3.5, -6) and the midpoint M(1.5, 4.5)?

How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-3.5, -6) and the midpoint M(1.5, 4.5)?
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artirw9f
Step 1
The formula to find the mid-point of a line segment give the two end points is:
$M=\left(\frac{{x}_{1}+{x}_{2}}{2},\frac{{y}_{1}+{y}_{2}}{2}\right)$
Where M is the midpoint and the given points are:
$\left(\begin{array}{cc}{x}_{1}& {y}_{1}\end{array}\right)$ and $\left(\begin{array}{cc}{x}_{2}& {y}_{2}\end{array}\right)$
Substituting the information we have gives:
$\left(1.5,4.5\right)=\left(\frac{-3.5+{x}_{2}}{2},\frac{-6+{y}_{2}}{2}\right)$
To find ${x}_{2}$ we need to solve this equation:
$1.5=\frac{-3.5+{x}_{2}}{2}$
$2×1.5=2×\frac{-3.5+{x}_{2}}{2}$
$3=\overline{)2}×\frac{-3.5+{x}_{2}}{\overline{)2}}$
$3=-3.5+{x}_{2}$
$3.5+3=3.5-3.5+{x}_{2}$
$6.5=0+{x}_{2}$
$6.5={x}_{2}$
${x}_{2}=6.5$
To find ${y}_{2}$ we need to solve this equation:
$4.5=\frac{-6+{y}_{2}}{2}$
$2×4.5=2×\frac{-6+{y}_{2}}{2}$
$9=\overline{)2}×\frac{-6+{y}_{2}}{\overline{)2}}$
$9=-6+{y}_{2}$
$9+6=6-6+{y}_{2}$
$15=0+{y}_{2}$
$15={y}_{2}$
${y}_{2}=15$
The other end point of the segment is: $\left(6.5,15\right)$