Answered

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The midpoint of AB is M(0,3). If the coordinates of A are (1,2), what are the coordinates of B?

Sagot :

Answer:

B(-1,4)

Explanation:

Given: The midpoint of AB = M(0,3)

Coordinates of A = (1,2)

We substitute these values into the midpoint formula.

[tex]\begin{gathered} M(x,y)=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}) \\ M(0,3)=(\dfrac{1+x_2}{2},\dfrac{2+y_2}{2}) \end{gathered}[/tex]

Equating the x-coordinates, we have:

[tex]\begin{gathered} \dfrac{1+x_2}{2}=0 \\ 1+x_2=0 \\ x_2=-1 \end{gathered}[/tex]

Equating the y-coordinates, we have:

[tex]\begin{gathered} \dfrac{2+y_2}{2}=3 \\ 2+y_2=6 \\ y_2=6-2 \\ y_2=4 \end{gathered}[/tex]

The coordinates of B are (-1,4).

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