The required other point of the given mid point is (-1, 1)
What is the midpoint of the two points ?
The midpoint of any points say [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] then the midpoint (x, y) of these two points is given by
(x, y) = [tex]\left ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right )[/tex]
How to calculate midpoint?
Here we have given that
The midpoint = (2, -4)
[tex](x_1,y_1)=(5, -9)[/tex] and let the other point is (a, b) then from above midpoint formula we have
[tex](2, -4) = (\frac{a+5}{2},\frac{b-9}{2})[/tex]
On comparing the coordinates we have
[tex]\frac{a+5}{2} = 2\\\\a=4-5 = -1[/tex]
and
[tex]\frac{b-9}{2} = -4\\\\b-9=-8\\\\b=1[/tex]
Therefore the required other point is (a, b) = (-1, 1)
This is the conclusion to the answer.
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