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BC has one endpointB(3,2) and a midpointT(6,-2). Find thecoordinates of theother endpoint, C. Thank you in advance!!

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We are given that BC has one endpoint B(3, 2) and a midpoint T(6, -2)

We are asked to find the coordinates of the other endpoint C.

Recall that the midpoint formula is given by


T(x,y)=((x_1+x_2)/(2),(y_1+y_2)/(2))

Where


\begin{gathered} T(x,y)=(6,-2) \\ B(x_1,y_1)=(3,2) \end{gathered}

So, the other endpoint C is


x=(x_1+x_2)/(2),y=(y_1+y_2)/(2)

Substitute the given values,


6=(3+x_2)/(2),-2=(2+y_2)/(2)

Simplify,


\begin{gathered} 2\cdot6=3+x_2,-2\cdot2=2+y_2 \\ 12=3+x_2,-4=2+y_2 \\ x_2=12-3,y_2=-4-2 \\ x_2=9,y_2=-6 \end{gathered}

Therefore, the coordinates of the endpoint C are


C(x_2,y_2)=(9,-6)

Bonus:

Let us verify whether we got the correct coordinates or not.


\begin{gathered} T(x,y)=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ T(x,y)=((3+9)/(2),(2-6)/(2)) \\ T(x,y)=((12)/(2),(-4)/(2)) \\ T(x,y)=(6,-2) \end{gathered}

Hence, we got the same midpoint as given in the question.

User Thiago Tanaka
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