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6.3.12
The coordinates of point T are (0,5). The midpoint of ST is (2,-2). Find the coordinates of point S.
The other endpoint is
(Type an ordered pair.)

Respuesta :

MrRoyal

Answer:

[tex]S = (4,-9)[/tex]

Step-by-step explanation:

Given

[tex]T = (0,5)[/tex]

[tex]Midpoint = (2,-2)[/tex]

Required

Find S

Midpoint is calculated as:

[tex]Midpoint = 0.5(x_1 + x_2,y_1+y_2)[/tex]

So, we have:

[tex](2,-2)= 0.5(0+ x_2,5+y_2)[/tex]

Where x2 and y2 are the coordinates of S

Multiply through by 2

[tex]2 * (2,-2)= 2 * 0.5(0+ x_2,5+y_2)[/tex]

[tex](4,-4)= (0+ x_2,5+y_2)[/tex]

[tex](4,-4)= (x_2,5+y_2)[/tex]

By comparison:

[tex]x_2 = 4[/tex]

[tex]5 + y_2 = -4[/tex]

[tex]y_2 = -4-5[/tex]

[tex]y_2 = -9[/tex]

So:

[tex]S = (4,-9)[/tex]

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