Question 212001
The coordinates of the point T are given as (10,18). The midpoint of segment ST has coordinates (5.-8). Find the coordinates of point S. 
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Use the midpoint formula:

The midpoint between points (x<sub>1</sub>,y<sub>1</sub>)
and (x<sub>2</sub>,y<sub>2</sub>), is the point:

M = ({{{(x[1]+x[2])/2}}}, {{{(y[1]+y[2])/2}}}),

Let the coordinates of S be (x<sub>2</sub>,y<sub>2</sub>)

We are given

M = (5,-8)

Therefore

{{{(x[1]+x[2])/2=5}}} and {{{(y[1]+y[2])/2=-8}}})

And we are given pt. T = (x<sub>1</sub>,y<sub>1</sub>) = (10,18)

Substituting:

{{{(10+x[2])/2=5}}} and {{{(18+y[2])/2=-8}}})

Multiply both sides of both equations by 2 to
clear of fractions:

{{{10+x[2]=10}}} and {{{18+y[2]=-16}}})

{{{x[2]=0}}} and {{{y[2]=-34}}}

So the desired point S is (0,-34)

Edwin</pre>