Answer :
The midpoint of a line segment is the point equidistant to the endpoints of the line. The coordinate of S is (2,-9)
Given that:
[tex]T(x_1,y_1) = (0,5)[/tex]
[tex]M = (1,-2)[/tex] --- the midpoint of ST
[tex]S = (x_2,y_2)[/tex]
To calculate the coordinates of S, we use the following midpoint formula:
[tex]M = 0.5 \times (x_1 + x_2,y_1+y_2)[/tex]
So, we have:
[tex](1,-2) = 0.5 \times (0 +x_2,5 + y_2)[/tex]
Divide both sides by 0.5
[tex](2,-4) = (0 +x_2,5 + y_2)[/tex]
[tex](2,-4) = (x_2,5 + y_2)[/tex]
Compare both sides
[tex]x_2 = 2[/tex]
[tex]5 + y_2 = -4[/tex]
Collect like terms
[tex]y_2 = -4-5[/tex]
[tex]y_2 = -9[/tex]
Hence, the coordinates of S is:
[tex]S = (2,-9)[/tex]
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