Mathematics: The coordinates of point T are (0, 5) . The midpoint of overline ST is (1, - 2) . Find the coordinates of point S Plz hurry if u can!!!

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The coordinates of point T are (0, 5) . The midpoint

jos0305

05.02.2022

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:

T(x_1,y_1) = (0,5)

M = (1,-2) --- the midpoint of ST

S = (x_2,y_2)

To calculate the coordinates of S, we use the following midpoint formula:

$M = 0.5 \times (x_1 + x_2,y_1+y_2)$

So, we have:

$(1,-2) = 0.5 \times (0 +x_2,5 + y_2)$

Divide both sides by 0.5

(2,-4) = (0 +x_2,5 + y_2)

(2,-4) = (x_2,5 + y_2)

Compare both sides

x_2 = 2

5 + y_2 = -4

Collect like terms

y_2 = -4-5

y_2 = -9

Hence, the coordinates of S is:

S = (2,-9)