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AB has endpoint A(-3,-5) and midpoint M(2,-1).Find the coordinate (x,y) of B.

AB has endpoint A(-3,-5) and midpoint M(2,-1).Find the coordinate (x,y) of B.-example-1
User Guus
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By definition, the formula to find a Midpoint is:


M=((x_1+x_2)/(2)+(y_2-y_1)/(2))

Where the coordinates of the first point are:


(x_1,y_1)

And the coordinates of the second point is:


(x_2,y_2)

Let be the coordinates of the Midpoint:


(x_M,y_M)

In this case, knowing coordinates of the point A and the Midpoint, you can set up the following equations:

- Equation 1:


x_M=(x_A+x_B)/(2)

- Equation 2:


y_M=(y_A+y_B)/(2)

Choose the Equation 1, substiutute values and solve for x-coordinate of the endpoint B:


\begin{gathered} x_M=(x_A+x_B)/(2) \\ \\ 2=(-3+x_B)/(2) \\ \\ (2)(2)=-3+x_B \\ 4+3=x_B \\ x_B=7 \end{gathered}

Now choose the Equation 2 and solve for the y-coordinate of the point B:


\begin{gathered} y_M=(y_A+y_B)/(2) \\ \\ -1=(-5+y_B)/(2) \\ \\ (-1)(2)=-5+y_B \\ -2+5=y_B \\ y_B=3 \end{gathered}

Therefore, the coordinates of P are:


B(7,3)

User Runmad
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